What do you mean by "relationship"? Exclusive? Long-term?
I don't know if I've had a relationship come out of online dating according to your criteria. Right now I'm less than two months into dating someone, and it's the longest I've dated someone from online. I've also never gotten to the point of having a conversation about exclusivity (although there were times when I was dating only one person and I'm pretty sure he was only dating me). To answer the question, I do think that people do reveal their personalities in emails. I think I usually had a sense of what a person would be like to spend time with based on those initial emails. BUT I don't think I had a sense of their relationship issues or emotional intelligence. I had a sense of what they'd be like as a person but not as a potential boyfriend.
Anyway, things change. People can be really into you and then suddenly not into you. I don't think it's always "game" in those instances. Sometimes it's just a matter of being fickle, or realizing that someone is not for you once you know them better or once you take them off that pedestal.
One thing I will say doesn't have to do with the quality of emails but the quantity. There have been a couple of times when the guy has not been prompt with his replies and, because I was really interested, I ended up emailing twice to basically find out "Are you still there?" In both of those cases, they replied to say, "Sorry, I'm bad with email" or something like that. But obviously if you have to work hard to get them to reply to emails, they're not that interested.