The rule would still apply, of course.
And yes, the game may still continue if neither of the players claims a draw. But if the game goes on for 75 moves like that, then it's an automatic draw regardless.
There are plenty of forced checkmates that need more than 50, 75 or even 100 moves. With best play that is. Noone would be able to perform such stuff over the board anyhow.
So, this is probably never going to happen in a game, but is there a position where it is theoretically possible to checkmate, but to do so, you would need to violate the 50-move rule? Simply, is there a forced checkmate pattern that takes longer than 50 moves, with none of the moves being captures or pawn moves? Adding on to this, if there were to be such a position, would the 50-move rule still apply or would the game be allowed to continue until checkmate is reached?