In general no. Most professional ballet schools disapprove, but it is fine for daily classes, especially if it is a black (or whatever color your school requires) sports bra. I Allways Wear one,...
There is no need to wear a bra under a sports bra, because sports bra has the function of supporting breast at right position, the key point is that you need to choose a good sports bra.
YOU COULD WEAR A BRA UNDER ANYTHING BUT... Some swim suits have bras like in them. And you could wear a bra under your swim suit BUT it would hart a lot. so don't wear one