I think, being sixteen and having been in a serious relationship, that young love is a "thing", but love is one of the most mercurial concepts in the english language, or any language for that matter, right next to the word good. It's all about perspective, I would say that there's many people that I love, as in a I care for them and would go through many a hardship for their benefit, although I don't necessarily want to get into their pants. In regards to sexy times, relationship love, I do also believe that teens can be in love, although the operative word is can, and there are many ridiculous hormone driven people out there claiming to be in love. Not just teens mind you. So I do belive in it, because yes, for the first few months of a relationship it's fun to let sex all sorts of shenanigans rule your relationship, but after the initail haze of a fantastic time passes and your hormone driven frenzy has faded but you're left with a deep passion for someone and as well as the desire to screw the hell out of them you can be happy just sitting next to them talking about some random bullshit or something that pisses you off or makes you happy, or just nothing at all and you can be next to them and just hold their hand and be a happy person, that's love, and anyone can feel it, just about anyone without some emotional issue.
In any case sorry to get all sappy, and to say it easily yes. It is most definitely possible and don't let anyone tell you otherwise, anyone can fall in love.