No, this shouldn't affect anything. It may hurt though. Or if you get a scrape, there is always a chance things can get infected. But overall, this is not dangerous or an issue.
If you were one of those girls who lived in a place where they remove female genitalia out of fear of the woman being sexual, you might lose your opportunity to have an orgasm. But not from being scratched by your boyfriend's fingernails. That said, I would tell him to learn to manicure those scraggly nails or there is absolutely no way they should be near anybody's clitoris. If he can't cut them, it's likely that he is not keeping them very clean either, and you're asking for an infection.