I've heard that all the stronger chess players (GMs and the like) are naturally able to play blindfold as a consequence of their chess visualization skills.  What's the minimum rating where this happens - can 2300s play blindfolded?  2000s?

And also, if I train to be able to play blindfolded will my rating increase?

I don't think there's a minimum rating that enables one to play blindfolded.  I've heard stories of 1800's being able to do it and 2200's not being able to do it, it's very person dependent.  But the odds of someone rated 1200 being able to play blindfolded is pretty slim.

I think training to play blindfold chess specifically won't help your rating or overall play very much.  Even if you are able to play blindfolded, if your chess understanding hasn't increased, you'll just play very poor moves without sight of a board.  For instance, say a 1200 is playing a 2400.  The 2400 is blindfolded and the 1200 is allowed to use the board, and move the pieces all over the board analyzing his moves.  The 1200 can theoretically see as far in advance as possible, but he'll still get crushed easily because his overall game understanding isn't up to par.

Instead of trying to work on playing blindfolded, I think your time would be much better spent working on your openings and middlegame transition/plans, studying the endgame, and analyzing GM games.  If you really force yourself to focus when studying and playing, your ability to calculate and "see" many moves ahead will get better.

It was my opinion that I doesn't help your chess at all. I've come back from that somewhat. It may help your visualization when calculating lines.

But there probably are more time effective ways to train this. I don't see the use in it

I think there are blind players at all levels. Plenty of blind people play.

The other thing I think it might help train is memory of games.  If you can play blind then you can remember the game and recognize patterns from it later on.

A good point, do you know where to find information about the ratings of visually disabled people?  I found http://www.americanblindchess.org/ratings.html however that is only for correspondence chess, which is not necessarily the same as playing "blindfold," i.e. a blind correspondence player might review the move history repeatedly, or set up the position on an analysis board.

I could play a game blindfold when I was c. 1200, before my first USCF tournament, so I think it can be done by pretty weak players.

I'm not very highly rated, but I find it next to impossible to play without seeing the board for longer than a moves. I have a weird thing with my brain where I lterally cannot form images in my head. I have an obscene amount of memory and prcoessing for words, but not images. Blindfolded playing can increase your chess skill, but not all people are able to do it.

I remember FM Hayward playing me blindfolded back when I first started playing chess. He had his back to me while he played someone else. I called out the moves and he called out the replies and won fairly quickly. Again, I was a beginner at the time, but it still impressed me that he could do this while playing someone else.

Playing blindfold helps develop analysis skills. 

Like any other skill, it requires practice.  I learned first by following - or trying to follow - the stronger players of my first club, who would gather at a tavern after the club (and I could get served beer underage by being with their group!) and play blindfold games in teams, and then by playing with my mentor/coach as we drove to out of town tournaments.

You go as far as you can at first, if you lose the position in your memory, you resign.  But you can go a bit deeper with practice, and then analyze those positions deeper, until finally you are able to play whole games well.

I think blinfold chess can help you. I remember GM Christiansen mentioning that after he did a simultanous blindfold play against amatures, he have a good result in the tournaments that follows.

I can play blindfold and I can bench press 200 lbs.

Playing through past games blindfold may be helpful too. I have done that with some classic games. Once I memorized the moves visually, I then did various exercises such as listing attacking or defending pieces in each position (similar to the Attack Training and Defence Training options in Fritz).

I had some college friends who could do it and they were not super strong - a bit above 1800 I think but certainly not 2000.

I am doubtful as to whether it helps your chess much.  There was a vogue for massive simuls a century or so back and some masters were competitive about playing the most opponents.  Quite a few of the simuls were played blindfold but after a while it became clear that the mental techniques developed to pull off these tricks damaged one on one playing strength.  Maybe the damaging techniques were solely associated with playing 100 plus people simultaneously but I would not be surprised to find that the blindfold aspect plays a part too.

Anyway massive simuls, blindfold or not, disappeared.

I could play blindfold when I had a rating of 1500.  I don't think it helped my chess playing at all, but did give me some severe headaches.  At the Amber tournament they play with a blank board in the "blindfold" games which helps a lot.  One tip if you want to try playing blindfold is to divide the board in quarters.  Each quarter board is identical consisting of 16 squares (4x4) with a light square on the left bottom and upper right corner.  When I visualize the board only a quarter is "in focus" and the rest of the three quarters are kind of fuzzy.   It is much easier to try to visualize the board a quarter of board at a time, and you can learn to follow a diagonal from one quarter to another (very easy with the two long diagonals).  Larry Christensen may find it useful for warming up for a tournament, I found it detrimental to my tournament play (hard to concentrate when you already have a headache at the beginning of a game).  In the old Soviet Union blindfold simuls were illegal as it was considered a health hazard.

Blindfold chess is NOT as hard as everyone makes it out to be, and yes it does help with calculation/visualization in regular OTB. 

My suggestion is to get the chess eye program and do 10 questions from each set of exercises every day, and play one game of blindfold against a computer once a day, alternating sides.

I play against Fritz and set the figures to blindfold, minimize the board, and just type in the moves.  Alternate black and white so you get a feel of the board from both perspectives.  I started out playing the easiest setting on 'friend mode' and am now able to beat 'tit-for-tat' regularly.  Adjust the strength so that Fritz will punish your basic mistakes (like taking pieces you have left en prise) but won't totally crush you.  My rule is that if I can beat a level three times in a row without making a blunder, then I go up to the next level.  You will make very very basic mistakes your first few games, but stick with it, and after a few games you will develop an internal dialogue about piece safety.  Once you make safe moves every turn and with bit of practice, you will eventually just see the board with minimal effort and can focus on more complicated plans/attacks.

In my opinion the strength of blindfold chess for beginners is that you HAVE to visualize the board as it will look on your next move, and you HAVE to ask yourself basic questions about whether your move is safe.  It also forces you to carefully consider the consequences of your opponent's move ("what is his pawn move threatening -- oh @#$%, he's hitting my queen!")  Piece safety and assessing your opponent's threats are the most basic elements of a good internal throught process in OTB (or any chess).

For more advanced players it helps you be more fluent in finding good candidates when visualizing a complicated variations.  You can stop at any point in your calculation, see the board clearly, and look for solid candidates. 

It is not that hard, and there is definitely value in it.  Just try it -- expect to lose a lot at first, but you'll see pretty fast that you can easily make it into the middlegame with all your pieces and pawns by asking very basic questions about piece safety and your opponent's threats.

It depends to what standard. I can manage blindfold but I would be playing 500-600 pts below my normal standard. Anyone who can play close to their normal level blindfolded is really impressive.

And the most impressive thing is simultaneous blindfold, believe it or not there are people who can do this.

If you practice, you can probably do it. I haven't seen real beginners do it, but more experienced players in the 1800 range, sure.

I can somewhat do it myself, but there are risks of serious mistakes later in the game.