It's a shame about U Mitford and her fascist nuttiness, because I do think it's an attractive name in itself. I kind of like the notion of "virtue" names, from a historical POV (though would not, of course, choose one that suggested expectations for a child's actual personality ... but I don't think Unity really does that).
I like the fact it starts with U, as well.
Would only use in fantasy naming, though, not for real baby. Especially now that Liberty et al are sort of middle-class trendy names - they have definitely acquired a bit of an eye-roll quality and that would apply to Unity as well.