I don't think it does. I think that should only occur if there is a clock winding down that cannot be stopped so that someone does not win on time in a repetition of moves.
when you CAN claim a draw (3x repetition, or 50 moves, etc) then the OFFER DRAW button should turn into a CLAIM DRAW button. is this not working for anyone? :)
If a situation arises that calls for a draw, such as repition of moves, does the option of declaring a draw appear on the screen?