Good question, and I think for most people - no.
There is a level of artifice on the net that changes the dynamics. I think a lot of social niceties, for example, are cast aside. Some normal social interactions don't really exist online. For example simple things like saying "good morning", or "how are the kids?", or "that's a nice dress". These things just don't happen.
Online discussions can also become incendiary much faster than in real life. I mean, if you go to a party, how often does the "Is there a God?" come up? Let alone politics, or many other topics. It's just not normal conversation. So we adapt, change in our interactions.
One could argue that our actual personality isn't changing in these circumstances, but I think it actually exaggerates bits of of our personality. In real life I think it's usual to be more level, and certainly more polite.