Yup! I'm a huge fan of anime (24 y/o woman) and have a boyfriend who never watched it before me. I've had him watch ones with normal depicts of woman (Fate/Zero, Death Note) and ones with the type of characters you describe (high school of the dead-it's hilarious in the depictions of boobs). I think most people who watch anime watch it for the stories, but there are some that have weird attractions to them. If he doesn't think of how they look in a sexual way and likes the stories, it's no issue. I'm not sure why anime would make you insecure, though, their animated characters.
However, if he reads a lot of NSFW manga of underage characters and gets off to it, I'd have questions. Manga and anime is entertainment, you can't really know what someone gets out of it unless you ask.