If a woman has sex one day and her regular period begins the next day (or even in the next few days) she is not pregnant.
You can get pregnant before your period, that is the time it is going to happen because a woman will ovulate sometime after her period. If you get pregnant then you will not have a "normal" period--because a normal period would be you getting rid of everything and your body will not do that when it is getting your body ready to carry a baby. But what can happen is to have bleeding during that time which can be mistaken for a period, sometimes it doesnt last as long or is light compared to a normal period.