No, photo film definitely can be affected by gamma rays, gamma rays were actually discovered using photographic plates. Flying on a few hours on the plane with your photo film will "expose" your film, but most of the time, the actual photo exposure will be a much higher "dose" of light, that you will not see anything the affect from the gamma ray exposure.
The concept of film is the same, expose to light to generate an "image". Photo film does not only selectively expose visible light and exclude everything else, as higher energy wavelenghts could also result in an exposure. Your dosimitry badge requires an ionizing radiation which causes the metallic salt to emit a light which is then recorded and used to calculate your exposure.
To answer your first question, gamma rays do "hurt" film and people. Mark Kemp answered your second question.