Consider this objectively drawn position that occurred in the Fischer vs Spassky 1972 match, game 12. Suppose this position occurred in a blitz game where Black barely has few seconds remaining on his clock. Black decides to give up the f5-pawn and instead sit comfortably with his pawns on f6 and h6 as follows-
[fen "8/5p2/6kp/p4p2/2B5/1P2PK1P/8/4b3 w - - 0 1"] 1. Kf4 f6. 2. Bd3 Bb4. 3. Bxf5+ Kg7.
This position is an impenetrable fortress. Because of the presence of bishops of opposite color, there is no way White can check the Black king or even try to win a pawn by attacking it. If White marches up the e-pawn, Black can simply capture. There is no way White can win. Black simply has to keep moving his bishop safely on the a5-e1 diagonal.
Now, since this is a blitz game and Black just has a few seconds left, White simply attempts to run Black out of time just by making legal moves without making any kind of progress. In such a scenario, would Black be allowed to pause the clock and claim a draw?