Without going into way over the head detail, the simple answer is yes pushing film will make the film more sensitive to damage.

This is because pushed film is more sensitive because the base image is underexposed which is going to compress all of the tones until there developed , and since the image is being pushed it means that those shadows are being extended so more highly susceptible to damage(or additional energy sources) as the amount of silver and dyes is less. Pushing film is basically extending the amount of time the film is developed so that all the tones can be expanded to achieve a full range of tones. This is done even for artistic reason/effects or because the person wasnt able to carry.