Can you have sex 2 days before your period, get your period two days late, and still be pregnant?

Yes, yes, and yes. A healthy woman in her reproductive years can become pregnant any time during her cycle, with chance being highest during/around time of ovulation and lower during active menstrual flow. It is hard to tell exactly when ovulation occurs and so timing is a very poor method of contraception. Best is to use protection (condoms and/or pills) at all time if u don't want pregnancy. Consult doc. Good luck.