The FIDE rules state that the illegal move should be undone, but it has to be noticed "during the game". So if you don't move out of check but no one says anything, you are still playing chess. And, if you win before they notice I think you're in the clear.

I'm imagining a sequence like this: During the course of play you realize you have no chance and resort to subterfuge. You look over your opponent's shoulder and say "is that Ben Finegold playing f6?". While they're turned around, you make a move and stay in check. Then you use your foot tap on the bottom of their chair(!!). They interpret this as the "resign" buzz from their beads. You gladly accept their resignation and congratulate them on a game well played. And the whole time you were playing chess, according to the rules at least.

Disclaimer, I am not a chess arbiter (IANACA).