No. The only draws you can claim are the 50 moves without a pawn move or capture and the threefold repetition of position. You have to claim them by hitting the draw button.
And if you can eliminate mating material (getting your opponent down to a lone king, etc.), you can let the clock run out.
If you're low on time, it would be logical to try and claim a draw in such a position, but under what grounds are you claiming the draw on?