No. She doesn't need that. We called them training bras. Tell her that when she's older you will revisit it but at 6 she doesn't need one and if she is cold, she can wear an undershirt or camisole/tank top. I think it's another marketing ploy and is working with some parents.
Now, when she's 10 or 11 and has to dress out for gym, regardless of what she actually has or not, I'll get my DD some bras because of her age and need. I SO wanted a bra when I was 11 to be like the other girls when dressing for gym. However, they will not be the molded cup bras my SD got at 10 (and trust me, the girl caught up so there was no need to fake it as a 10 yr old).
Oh, and if you think uniforms completely get rid of competition, etc. think again. Ask a Catholic school girl (my freshman roommate was one) about the skirts that were rolled to be just a little shorter or the shirts and sweaters that were a half size smaller. Dealing with these things starts at HOME, regardless of what they wear out.