This has probably been debated to death already, but I feel like answering..
NO. That cannot happen. You CAN have sex while on your period that, a few days later, will result in you being pregnant. Sperm can hang around in your vaginal canal, uterus, or fallopian tube while you are on your period and if you
happen to be a woman who ovulates earlier than most (and the chances of that aren't particularly high), then yes it could result in pregnancy. But an egg nor a fetus can live in a uterus that is shedding its lining, it is impossible.