This is a difficult question as 'online behavior' in EVE especially is in the eye of the beholder.
Someone might take offense to my blapping your ship in highsec that you've saved up for for the last three months, or I might wardec or implode your corporation and cause a mass exodus of your pilots. Meanwhile I'm generally super friendly in an ooc and 'game' chatting basis. I don't see turning your little grey boxes into little red boxes on the screen as things to get upset about, but for people who who do a lot of our behavior could be seen a bit 'antisocial.'
I generally ignore anyone and anything that seriously argue this. PVP activity in a PVP game is not 'antisocial' behavior, that's the same as saying that all FPS gamers around the worlds are mass-murdering lunatics.
My own personal belief is that, yes, behavior in a game can reflect RL behavior. If some random guy that joined my corp 1-2 years ago that I don't know IRL robs said corp (good luck with that btw, and well played) I wouldn't mind overly much, besides the obvious in-game reactions. If an IRL friend of mine in my corp who I've known for a decade or more and who has been in my corp for years jsut takes everything and splits, there will be questions to follow IRL, and there would be consequences. "Only guy you can trust in-game" and all that.
Players that do whatever they can to give you the impression they are not playing a GAME per se, but are genuinely out to hurt you as much they can or make you quit the game? Griefers who make no secret they want YOU to suffer and be harmed, sad assholes who encourage their fellow players to grief other players into ILR suicide and suffering?
All these are indicators of the kind of sad prick IRL that I don't respect and don't want to know.
Being antagonistic or in competition in the confines of a game is one thing, taking the focus into harming the player is another entirely, and earns you no respect. So I'd go with yes, it can be reflective of IRL personality.