This is not really how it works, at least not internally. For instance the record for blindfold simultaneous games is 48. Playing that by anything even remotely like conscious memory would probably be impossible. If it were simply a game of conscious memory then a highly competent memory competitor should be able to play (even if to a poor standard) multiple blindfold games, yet in reality he'd probably be unable to play a single one - even if he is entirely capable of memorizing a deck of cards, which is vastly more 'state' than a chess position. And vice versa, test a highly competent blindfold player in a general memory game and he'd be unlikely to do much better than above average.

Chess, for a stronger player, is very much like a language - in fact it uses the exact same area of the brain. It's like when you read these words, you're not consciously thinking at all - the meaning just comes to you immediately. And in fact you could trivially recall everything I said (even if not necessarily verbatim) if you just thought for a second or so. But simultaneously it's not like you actually made any effort whatsoever to memorize it.

So how long of a conversation could you hold with yourself in your mind? Practically endless, and you could probably reconstruct the overwhelming majority of it on demand. It's the same with chess. Meandering around in your mind to positions of an arbitrary depth is not difficult for a strong player. And the person I was responding to felt that a player writing down some analysis to move 20 would be some meaningful form of cheating. In reality, I'd absolutely love for my opponent to be able to write down their analyses. It'd waste just a monumental amount of time and afford no advantage whatsoever. It'd be akin to you writing down the conversation from your mind.