It can happen. My little sister is a triple legacy (mom, aunt, and grandma! sheesh!) and when she went through recruitment here, some of the sororities heard she was a legacy and pretty much snubbed her.
Well, that only reaffirmed that she should be Alpha Phi.
But in all seriousness, it can happen. But it was also extremely well-known that she was a legacy because we were very excited about it (her mom sent in a rec... and I think it was like the first rec we'd ever gotten).
I'm sure if she doesn't yap about it to everyone within earshot, she'll be fine.