I think it is an interesting question. Aside from consent, playing against an anonymous cheater is indistinguishable from playing against a better player. Presumably people are elo matched so it should not matter
It is definitely not indistinguishable, both because "someone with this rating shouldn't be winning like this" and because engine moves look very different than human moves, especially at lower ratings.
At top levels it gets closer -- often human play is compared to engine play and people will discuss which moves were 'engine-like' vs 'human', and a significant achievement would be to play the engine moves on every turn. Although it should be said that engine moves are not always necessarily the best moves positionally, nor the moves with the highest win % versus a human (because you can 'trick' a human, whereas the engine can't trick itself so it will never prefer a move like that)... but they are always the best moves tactically.
In middling ratings, if I was allowed to look at the engine (in a Lichess replay for instance) I'd guess I can tell a player using the engine with 99+% accuracy. People _always_ lose on tactics (or misplayed opening lines, misplayed endgames, etc). Engines never do. At high ratings I assume this goes down, especially if the players are playing 'boring' draw-ish lines, in which the best moves are fairly obvious most of the time.
Thanks for breaking down how this would actually work in practice. As an amateur player, I don't think I personally would be able to tell the difference between playing a much better player and a good bot, or a bad player and a bad bot.
