When my kids were young, the pool at the nearby park offered swim lessons. We told the kids they were going to learn.
My daughter objected. She didn't want to learn how to swim. We insisted. We didn't care if she ever spent time in the pool again, but she was going to have a basic knowledge of HOW to swim. We didn't care if the nearest ocean was 500 miles away, or if the local lakes were barely deep enough to wade in. In our opinion, knowing how to swim is an essential skill.
Now, at 26, she still has no interest in water sports or pools at all, but at least we know if some idjit thinks it's funny to push her in when she's walking by a pool, she'll have at least enough skills to get herself back to the side.
Whether you take your GF on a dive or not, I strongly encourage you to recommend she take basic swim lessons at the local Y, or other such place. Along with the others here, I think it's a bad idea all around for someone who isn't competent at swimming to try diving. There's just too much potential for disaster if something goes awry.
My wife and I are both excellent swimmers and comfortable in the water, and I still anticipate that first certification dive in a few months to be a bit stressful. I've talked to other divers and heard stories, so I know what the potential is for nerves to affect the reactions. I could not imagine adding the stress of being a non-swimmer to that mix.