Trial and error learning? I'd say with average talent, no studying, and no feedback with any game...class D. Pure guess.
How far can experience alone take you?

So you're asking:
Average person
No study
No analysis
Only games
Nothing beyond piece movement and playing games.
I think mid to high class D is a pretty good guess actually. Maybe around 1300 USCF after a few years and a few thousand games (whatever it works out to).
Class A no way. If they're really talented, then sure, class A no problem. But the average person wouldn't even come close.

Hmmm
Honestly, Ish own dozens of books on Chess .. have flipped through them a few times, found them infinitely Boring and put them away for "later"
Ish, as Teary's pointed out, is a lower player .. for now .. Good minutes and Bad weeks .. that sort of thing .. However, this is with a GooglePlex of other things going on/getting in the way
If given proper time, Anyone "can" improve .. Whether or not they WILL is another story
In this query, the Importance of "Non Resigners" is showcased .. how better to learn to Improve than to play Complete games .. whether Winning or Losing

One final? point
One would imagine that Many Famous Chess manuvers were Orinigally formed/learned through Experience .. Does that take away the value of taking the Time to Learn these differing stratagems?? NO, not in the least ..but Experience does count "for something"

Capablanca did it
So you are saying that Capablanca never recieved any lessons or instruction from anyone or anything at any point in his life, and that he never studied at all in order to get better?
I think that is quite a stretch. Capablanca perhaps didn't prepare like he should have before big tournaments and matches, but that hardly means that he never studied or analysed games at all.

There were GM strength players in the past before there were any chess books (beyond basics) or even a GM title because they had a great talent for chess and studied in other ways (analysis, composing studies). So in many ways they don't represent the type of situation the OP is asking about.
OP is asking about the average person who doesn't "click" with chess and yes, also has many other things going on in their life and at the same time isn't trying to get better. They just play chess every day without doing anything else, everything they learn they have to discover in that one game while they're playing for themselves. No analysis, no practice, nothing. After many years and thousands of games, I think that takes an average player about as far as 1300 USCF.
Throw into the mix a casually worked though book (75% read) every 2-3 years, a few tactical puzzles whenever they feel like it and looking up a few opening lines to get more comfortable and over a number of years you have your average American adult club player at around 1500 USCF.

A lot of quotes and stories from great players (e.g. Capablanca) should be taken in context. I don't believe that Capablanca never studied and was just a playboy throwing parties all the time. It makes for good stories though.
You think he really corrected his uncle on a knight move (or dad, which was it) at the age of 5 without having ever been taught the rules? I doubt it, but these stories he told built a personality. I think he was just a self promoter that way.
Just on your own skill you will always be between 1200 - 1500.
More you play closer to 1500 you'll get and your ratings will fluctuate between 1300-1500.
1500-1800 is another step which you need to sit and study and for everything beyond 1800+ in addition to studying you have to have lot of talent and just fanatical dedication.

Capablanca did it
So you are saying that Capablanca never recieved any lessons or instruction from anyone or anything at any point in his life, and that he never studied at all in order to get better?
I think that is quite a stretch. Capablanca perhaps didn't prepare like he should have before big tournaments and matches, but that hardly means that he never studied or analysed games at all.
Thats exactly what i'm saying look it up. The only study he got was just watching others games not writing it down not with commentary but just watching. Leonid Stien reached NM Stregth doing the same thing and in the oxford compainion of chess they say Ruben Fine reached expert stregthn doing the exact same thing.

Just on your own skill you will always be between 1200 - 1500.
More you play closer to 1500 you'll get and your ratings will fluctuate between 1300-1500.
1500-1800 is another step which you need to sit and study and for everything beyond 1800+ in addition to studying you have to have lot of talent and just fanatical dedication.
Will let you know when We get there

What comes to my mind, regarding the OP's questions, would result in a panzer.
I think that the truly great chess players of all time were not just "average" people. Some people have a greater affinity toward, say, playing basketball than do others. Same with chess.
The second thought is...why would you think you could be great at almost anything without training and paying your dues...violinist...golfer...President...oh...never mind...forget that one...
Is the question really: "How can someone with a 100 IQ who is lazy, or otherwise too preoccupied to study, serve an apprenticeship and work their way up the ladder...how can they putz around and be really, really good?"

There is a HUGE limit to how much you can learn on game experience alone. A post-mortem can teach you infinately more than any game experience in my opinion... an absoulutely average person will not get very far at all on simply empirical chess, there are simply far too many things that must simply be dogmatically learned. Take the example of the basic endgame mates- they are the bread and butter of endings, if you cant mate with a queen and king you are in serious trouble yet I know of no-one that "empiracally" learned the tecnique. There are simply far too much things you simply have to be told or read from a book, it would be generous to hope someone without ANY training could reach even 1200 USCF.

>>I believe 95 % of population can reach atleast 2300 ELO with good enough motivation.<<
I am probably one of the least likely around here to become "speechless". This though, does the trick.

i've learned soley through playing an watching the odd vid on this site. granted i'm not very good but i continue to progress, so i my opinion, as far as you want. playing strong players is the best tool for learning. let them read the books an show you on the board
Dude I live in real - not virtual word - if you're average guy making money by going to work 5 days a week or if you're younger and going to university and can get up to 2300 with little work in chess you would be in Guiness Book Of World Records.
By the way WakItDown what is your chess rating and what is your age?

Depends on the chess venues you visit. If you swim with sharks at local clubs, you will sponge tons of information assuming the stronger players offer/agree to go over the games with you. Even if you are not going to "listen" to them (being the deluded dreamer that you are :) )... chances are that a few of them will say something like "Don't do XYZ" and that has a tendency to stick when you are stewing over your loss.
Hypothetically, an average young man (or woman for pc), just suddenly decided to start playing lots and lots of chess while knowing only the basic piece movement (couple of games a day seven days a week). However, throughout all of the games played, the person never once studies any written material on chess, never watches any videos, never listens to any lectures, never practices anything outside of real games and never analyses any of their previous games.
How far do you think such a person could theoretically progress as far as skill level goes? Do you think that there would be a limit to how far they could go, or could they eventually reach a high level (such as A class or above) with some x thousand number of games?