How good at chess could you become without playing a single game?

There are people that can study math, say, for hours and hours, ace all the questions, know everything inside and out ... and still fall apart on exam day.  The pressure gets to them.  They need more exposure or special test-taking training, and they would never know this if they never took a test.

The same is true for chess.  There's a world of difference between theory and practice.  I've recently gotten into blitz after a lifetime of correspondence, and it's amazing the difference.  I am facing people with blitz-specific openings at time, filled with traps or bizarre castling Queenside set-ups just because.  These aren't good openings, but they pose certain practical problems, and I have very little experience with this.  Add in the ticking clock and I've lost a number of games I had no business losing, but that's the difference between theory and practice.

I have, unfortunately, never played an OTB tournament game, and though my online rating is over 2000, I doubt I seriously challenge a 1800 or even a 1600 rated player with all that experience.

SmithyQ, you don't exactly fit the profile of the "Never Played a Game" Player in the OP since you have played a lot of online chess, but I do think you would do fine in OTB tournament play against 1600s, scoring at least 50%.   I have seen your annotations and analysis, and you are underestimating yourself.

There's a good chance I understand chess at a 2000 level (or whatever), but I doubt I can perform at that level OTB, and certainly not instantly.

It's much easier to play chess in your favourite chair, leaning back with a cup of tea and analyzing as fast or as slow as I want.  That's not how OTB works.  Or if it does, then I'm missing out.

The rules for the upcoming WC match should stipulate thst each player may bring their favourite chair.

Sure, due to nerves, if you want to say some people will fall apart, and play drastically worse than their best, I'll agree.

If you want to say others will play a few 100 points below their best, I'll agree.

But the OP is sort of asking for a maximum. Someone with strong nerves and having already gone through difficult life experiences, for example, may not care at all and be able to play their best.

Someone needs to explain me the purpose of training for a game you do not intend to play even once.

To quote the owl in the tootsie pop commercial:

The world may never know:

A player needs to learn how to respond to sub-optimal moves, and to fight. That can only be learned by playing the game. You definitely can't become a professional level player without playing the game. 

In fact, I've had several students who could solve almost any puzzle they were presented with, but couldn't break 1600 in competition until I helped them. 

Sorry for being so random but...

Well, yeah, regular old analysis will involve searching for what to do against all sorts of moves.

And I doubt your students studied for 10+ years without playing a game, because that would be insane.

True, every student I've had save one loved playing. The other student was actually interested in the history of the game and the architecture of the pieces. He did his IB diploma thesis on the art history of chess. But even he played occasionally. 

By the way Leo Hirshfield was the tootsie roll, not the tootsie pop

This is just hypothetical and I do not mean for it to be realistic and even if it was, I certainly didn't mean that the player not actually play chess to avoid losing games. It is just for opinions, which I have gotten very many and varying opinions too.

Paul Morphy went from watching, learning the moves to good all at the same time according to stories about him.

I saw him this morning coming out of Walmart eating a bag of donuts.