I wear sports Bras regularly, and It hasn't stopped me from getting a C-cup. There are also two types of sports bras ones that have shaped cups and ones that don't, the ones that don't tend to squish your breasts a bit while so long as you have the right cup size the ones with cups don't. I wear both types.
The ones without cups still have a band size, while a 38 fruit of the loom sports bra (the ones that come in big packs) haven't done anything bad, I would imagine going undersized would basically be like binding. So just be sure of the size of the bras.