Yes, people can live without one.
You can learn a lot about that role by watching someone who’s been pulled over for drunken driving, Schmahmann says. “The state trooper test is a test of cerebellar function. So the effect of alcohol on cerebellar function is identified by everybody who’s ever done walking a straight line or touching their finger to the nose.”
https://www.npr.org/sections/health-shots/2015/03/16/392789753/a-man-s-incomplete-brain-reveals-cerebellum-s-role-in-thought-and-emotion
As far as the common trope that you live a mostly normal life:
I guess it depends on what you consider normal. I would think that going though life as if I was perpetually very drunk would be a drag. I suppose you could get used to it; actual drunks do.