Yes, but she did not when we first met. I took her on a couple of dive trips and she would hang out on the beach, read books, go shopping, whatever. Sometimes there were other non-diving SOs for her to hang out with. I asked her if she was interested in trying, but never tried to convince her to. Eventually, after snorkeling and hearing us talk about diving, she decided to try it. She tried a resort course in Cozumel, then took classes at home, and did her open water dives in Little Cayman. Sometimes she has ear trouble, so she stays behind and I dive. Luckily, as long as she has something to read, she's pretty happy, so I don't have to work too hard finding a place with non-diving attractions.
I totally agree with the earlier comment that you should not try to convince her to dive. It will probably backfire on you. I have seen people in classes who were doing it for the SO (or dad, or whatever), and they were not having a good time or really learning to dive. Try to arrange a vacation in a place you can dive and she can enjoy herself as well, and then see what happens. Cozumel is pretty good for that, or Grand Cayman (although it is pricey). Playa del Carmen is a good general vacation spot that has decent diving. There are lots of places that could keep both of you happy. Just don't drag her off to someplace like Little Cayman (a nearly deserted island where there is nothing to do but dive), unless she will be happy with a hammock and a book for a week.