Yes, of course it's possible. It's best to spend time together in person and see how you get along. If you both agree, you could just take the plunge. People throughout history have married people they did not know well in person. It takes a strong commitment, though, on both your parts.
It's one possibility. But another possibility you should realize is that the person might not be who they are claiming to be. Manti Te'o carried out an online relationship for years. It turned out to be a guy just pretending to be a girl. Don't get hoodwinked.
lol yeah, I have friends that met through irc (it's a chat thing and super old) about 14 years ago. The guy traveled from North Carolina to California to meet her. They're still happily married with 3 kids.
As for internet relationships, I think trust but verify is slogan I would use. You're going to want to meet and if the person keeps putting it off, I would have serious doubts the person is real.