That is also to say if the sub can handle that amount of power without decreasing it's undistorted linear output too much. If a sub is already about to bottom out at 1,000 watts in box X, adding 500w is just going to make it bottom out more often and it will sound like crap. The sub is already reaching its maximum undistorted output level in that box with 1000w. That is the entire reason you don't need to push a sub to its thermal limits in every single box.
The long of the short of it is, as always, it depends. In a sealed box, it is more likely that the woofer can handle the power, but it may also help in a ported box with an extremly long throw woofer too, or one that has a very stiff suspension.