Last Day of Menstrual Cycle

I would say no. In order to get pregnant, you have to ovulate. Ovulation begins around the 14th day from the first day of your last period. So, say your period lasted 6 days and you had unprotected sex right on the 6th day, ovulation wouldn't begin for at least another week.
Live sperm remains viable in your body after ejaculation but only for a few days.