In matters of usage, everything is permitted, but not everything is correct.
We're allowed to begin sentences with upside-down question marks if we so choose, gleefully flexing the muscles of our free will, but that doesn't make it correct in English usage.
In this case, though, I regard the initial conjunction as grammatically correct. And as you'll find in Nohat's excellent answer to this question, many leading grammarians agree.
Don't let it stop there, though, because your question implies a larger one which I do find interesting: should the context of online communications be regarded as more akin to prose, or to speech?
There are two angles to look at this from: what is common, and what is correct.
Common usage in online forums, e-mails, and chats is predominantly conversational in tone. The majority of people on the Internet are treating it as a conversational context, not a written one.
This is a case where the rubrics of correct style are not yet in harmony with the popular usage. The major English style manuals continue to hold that a written word is a written word is a written word.
In order for harmony to be achieved, either the rules or the common usage will eventually change. If there's a bookie willing to take the bet, I'll lay my money on the rules changing first.
Why? Because we don't have village squares anymore. There's a reason we call many online communities "forums" - a reference to the original Roman Forum. The Internet is the public commons of the modern day, and I fully expect it will continue to be more conversational in tone than most other outlets for written expression.