The short answer to your question is NO. If you are having sex, with or without birth control, there is always a chance that you can get pregnant. So when you ask if it’s impossible, NO. If you ask is it improbable, then the answer is probably yes. It is less likely for a woman to get pregnant if she is not ovulating.
Also, having a period is not discarding a fertile egg…First of all, if an egg were fertilized, you would be making a baby. So what I think you mean is an unfertilized egg. Anyway, the material that you lose when you have your period is the lining of the uterus wall, not an egg. This is a common misconception that having your period is expelling an egg that was not fertilized by sperm. If an egg is released from your fallopian tubes and NOT fertilized, it dies and gets absorbed back into the body. Then, your uterine lining comes out as menstrual blood.
This is probably way more than you wanted to know. Check this out for further info:
http://en.wikipedia.org/wiki/Menstrual_cycle