No, as very few women ovulate during her menstural cycle.
Clysta is right. During your period your body is shedding the lining of blood that it would use to protect the baby. A woman's body very very rarely ovulates during this time. You get a period because there's nothing there, then the cycle starts all over again.
I read a book called Taking Charge of Your Fertility. It has a ton of information on getting pregnant and avoiding it and all sorts of stuff. I learned so much from it. Its worth looking on amazon for. Normally can get books cheaper on there or google it too. Good luck.
Its not impossible but unlikely. As most of the gals have said you generally don't ovulate whilst on your period therefore making it unlikely you will fall.
Buying Taking Charge of Your Fertility is great advice!