Marcus Ian , Jul 10, 2011; 06:31 p.m.
It's certainly possible. I've done ones in which very little flash was used, and I probably could have gotten away with none at all.
The more relevant question perhaps is it advisable. In answer to that, I would say a completely unambiguous no(!). While you could explain away (and perhaps very reasonably so) no flash in many, if not the vast majority of shots (depending of course on how you shoot), I find it highly unlikely that there aren't always going to be some instances where flash will be either required or at least helpful, whether it's using the flash as fill to break up facial shadows in harsh daylight, or bouncing it to freeze motion later in the evening. I can't say I've ever been to a wedding where a flash didn't at some point become very very very helpful in making beautiful images better.
As a further comment, this isn't your personal work. I hate flash when I can avoid it, but when somebody's paying me to get the best pictures I can, then I feel obligated to get the best pictures I can take given the limitations of the setting, rules, proper etiquette, and portable equipment. Flash is an essential part of that, and the inability, or unwillingness, to do that is completely unprofessional.
In a nutshell, I guess I'd summarize with: Yes, but don't do it(!) :-)