Could it be healthy for my girlfriend to experience pain and to bleed during intercourse while on the Depo-Provera shot?

Bleeding. Post-coital bleeding (bleeding after sexual intercourse) is most likely related to a vaginal tear. A history of painful intercourse strengthens the suspicion. The tear can be small or extensive, so if there is prolonged or heavy bleeding, an evaluation with a doctor should ensue. There are no health benefits to this scenario.