From what I know, it is possible but unlikely. Usually, a woman will not concieve from intercourse during her period because eggs only live 12-24 hours and therefore they have usually died before menstruation starts (10-16 days after ovulation for most women).
However, it is possible for women to ovulate very soon after their period, within the 2-5 day window in which sperm can survive. This means sex during the period can result in conception. Very occasionally women will ovulate before their period finsihes (especially with long periods). It is also apparently possible to mistake ovulation for a period, as women can bleed during ovulation, especially if they are stressed. Sex would then obviously be likely to result in conception.
I don't know whether these factors would apply in your specific case because you are using BCP's. I assume that the bleed you will be having is a withdrawal bleed, rather than a real period as such. I expect that you would be unlikely to ovulate during a withdrawal bleed because it is essentially a bleed caused by a sudden drop of hormones, which is not the ideal time for ovulation.
Having said that, these are only semi-educated guesses! I have never used BCP's so I am definitely not the person here who can give you the best advice.
