Yes you can wax while you're pregnant!
However, if you plan to wax while pregnant, you should start early on. While you're pregnant everything swells downstairs, and the increased blood flow to the area will make it more painful. Personally I wont do a first time Brazilian Wax after a woman is in her 2nd trimester, simply because I don't want anyone to have a horrible wax experience. I'm more than happy to even do my Extended Bikini Wax which still cleans mom to be up nicely.
Of course, if you've been waxing for years, you can 100% wax the entire time that you're pregnant. After giving birth you'll bleed for awhile and it's not a time where you feel really comfortable, so keep on waxing right through! I tell my clients that the standard 6 weeks for a vaginal birth or 8 weeks for a C-section are how long we need to wait for the first wax after baby arrives.
Of course, if there are any complications, you should speak with your doctor, we always want to be on the safe side!