Obviously, it's possible, as one can see from the many civil discussions that occur in this NG. The effect of anonymity is that it also permits many un-civil discussions, as one can also see from this NG.
Perhaps one might more profitably explore, what are the benefits of civility and what are the benefits, if any, of incivility?
IMHO, as one who enjoys the format where both kinds of discussion are available, I'd have to say that both have their place. I realize that what I have to say will infuriate a lot of racists, crypto-fascists, war-mongers and militarists, for which I've received my fair share of abuse, up to and including death threats. That is how they operate, and nothing will change that. In fact, it is probably beneficial that at some point the mask comes off and you can see what these ostensibly rational folks are really made of. In a fascist Amerikkka, if and when it comes down to that, these are the folks who will be the jailers, mercenaries and torturers required to keep dissent in its place.
Anonymity permits more than mere incivility. It also permits the expression of highly unpopular (in some places) and even dangerous views. While anyone can openly denounce the "evils" of "terrorism" without any more fear than he or she would have of praising mom, apple pie and the flag, some views are much more dangerous for the speaker and would probably wind up suppressed if not for the protection of an anonymous internet.
So, yeah, civil discussion IS possible and in fact thriving on the anonymous internet.