It is a cool position but a ridiculous question if you stipulate that there is time trouble. Even a grandmaster could have trouble with queen versus rook in time trouble and I read on wikipedia that with 3.. Kb2, it can take 26 moves to force mate. Saavedra position
If such a decision ever occurred, it was only in a short story, where both sides were enjoying brandy and cigars.
As an example, below is the famous Saavedra Position:
Just wondering, which line would you pick? Would you take the objectively best choice of the Q vs. R ending and try to prove your opponent can't win it or go for the stalemate swindle? Its a hard decision, especially in time trouble which is common in the endgame. This position isn't exactly the point (since most strong players have probably seen it and at high levels you would probably just pick the Q vs. R ending) but the general concept is, not sure if I'm phrasing this properly.
Maybe I should say something like a tricky, but objectively worse continuation than the best continuation (which still favors the opponent quite a bit).