Have you ever heard the term "bonding experience"?
When you do something really strenuous/difficult/pleasurable/meaningful/exciting --something intense -- with someone, you start to feel closer to them. This applies in all parts of life, not only dating, and with all sorts of activities, not only sex. It's something you've probably experienced before, with a roommate at summer camp or something like that.
Sex has an effect like that, except a whole fucking lot more. You will think and feel a lot of things you didn't expect to; everyone does, it comes with the territory. It happens whether or not you're fifteen, but some people don't think fifteen-year-olds can handle it, and, frankly, they're wrong. However, it is important, I think, to have a good social support network. Most fifteen-year-olds are not prepared to talk to their parents about their sex lives, so I should say, it is really important that there be some people who you could talk to, even though you probably won't want to, just because you might want to, and that kind of isolation really fucking blows.
There is only one thing that can really ruin your first time, which is simple: if it sucks/is painful/frightening. And this can happen at 23 as well as at 15. Suggestions: give each other head at least once before you try to have sex, cuddle, learn to have fun touching each other, etc, make sure that you have respect for each other/feel comfortable making the other person feel good/neither of you is going to try to act like a pornstar. Because, well, if you can do all that, you're most of the way to sex, really. Remember that you deserve caring and attention from your partner and likewise.
So I guess I'm the only 'yes' vote, but... consider yourself warned.