Absolutely. I lost my hair at your age, give or take. And by lost I mean it turned rather awkward and I decided to get rid of it all. The main difference now to before is that I have to be the one saying Hi to girls before they're interested in me. Or go on the dancefloor in a club as opposed to just drinking with the buddies.
I guess reality is that in the vast majority of cases it makes you less attractive but by no means does it make you unattractive. Furthermore if you're not bothered by it (and I know any balding guy would be, losing your hair is pretty harsh) they won't be bothered either.
If all it take for her to be turned off is less hair you aren't loosing anything by not having her in your life. I was 21 when my first wife told me I was thinning noticeably. I've had a bit of play in my day and married now to my second wife for 18 years. So do girls like guys with little to no hair? Some will and some won't. Choose wisely