Not really.
There's a classic UK children's book called Ballet Shoes about three stage-school sisters, in which
Posy is the youngest. It's a nice book and a good association, and the only one I have for
Posy as a name. But then there's 'posey' as in pretentious, and 'po-faced', and it's all very well being a sweet little bunch of flowers when you are a child, but it's hard to imagine on a sensible adult woman of mature years, unless she were... a bit ditzy.
In short, I wouldn't use it and think it's probably better as a childhood nn, if anything.