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.
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?