I've read that precum does not contain sperm, as it's made in an entirely seperate gland -- the only sperm that can be found in precum is from a previous ejaculation, where semen is picked up and then expelled. I've also read that urination kills sperm in the uretha that might be left over. I could be mislead, however -- please correct me if I am under the wrong impression.
So you're saying that, even if she experiences possible "side effects" from pregnancy, the pregnancy test will not be accurate?
As far as waiting until after her period, there is a strong chance she won't even have a period at all while on the shot, so it will be extremely difficult to gauge whether or not she's pregnant based on her period.