If I had to describe the series, I'd say something like: first a stand-alone, somewhat gruesome but rapidly-paced and gripping detective novel. Followed by a conspiracy novel / thriller duology, with exactly one character with depth: the unattractive, antisocial, violent, somewhat amoral Lisbeth Salander (she's already in the first book, obviously, but in more of a supporting role there). Her womanizing, sensitive, supposedly perfect partner/friend/occasional bedmate Mickael is little more than a cardboard character. The conspiracy part is fairly entertaining, at least in book two and the early parts of book three, after that I was less impressed.

So if she likes detectives/thrillers and doesn't mind that the plot and characters don't have much depth, yeah, she should like it well enough - there's a reason why those books have sold such ridiculous numbers. Except maybe if she has strong political views - Larsson was rather solidly left-wing, and Swedish left-wing might be a little far for most Americans. There's a lot of ranting at the system under the surface in those books.