Maybe not Gryffindor in specific, but her friendship with Harry and Ron in particular. You'll remember that they weren't good friends before the "cave troll incident" on Halloween, first year. Perhaps if she hadn't become friends with them, she'd have turned out a bit more like Percy (which is both a good thing and a bad thing, kinda like being appointed to any one of the houses).

OTOH, where, then, would she fall on the "social" scale, which is just as important to teenagers? Maybe she'd become friends with Ravenclaws, maybe not. Maybe she'd buddy up with Neville, maybe not. She probably wouldn't spend time with Lavender or Parvati, because they seem like giggly, "glossy magazine" girls, if you know what I mean, while I don't think anything will make Hermione completely stop being bookish, clever, and even political.