I know heaps of people who got involved online, assured me by high and low they had met the most amazing person, only to be heartbroken shortly (or less shortly) after. Unfortunately I'm sure most of us know lots of people in this situation, or have been there themselves.
I know 3 couples who met online at the library ad got married (and still are married). Not that marriage equals a 'happy relationship' per se, but it does at least constitute a long term commitment.
I know only 2 people who met here at the library and have a solid online relationship for about 2 years now. From the onset, they agreed to keep it online only. I'm sure there are more people out there, with successful longer term online-only relationships.
In my personal opinion, I believe 'happy online-only' is possible. I believe happy marriages are possible. Call me naive, but I even believe winning the lottery is possible.

Hoping you'll find what you're looking for.
avi