In my personal view, again I am not an AVRT representative, I can deliberately allow a TINY amount of alcohol to be ingested IF there were a purpose behind doing so. It is just an odd question, because there are usually alternatives to alcohol in any given situation.
I can think of some examples: medicinal tinctures with the medication dissolved in a tiny amount of alcohol (although uncommon to find these any more); I had a special alcohol-based mouthwash prescribed for swishing and not swallowing after oral surgery, and I accidentally swallowed some of it -yuk; I make a stew that has cooking sherry in which the alcohol cooks out, but I'm not going to try to measure it to find out if any traces of alcohol remain in it. Stuff like that.
Other than purposeful alcohol consumption in trace amounts for a valid or prescribed purpose, I can't think of any reason to ingest alcohol.
So, maybe the question should be, if I were forced to drink some alcohol in any amount, would that change my standing as a non-drinker? NO, in my opinion. I would still be a non-drinker. Being a non-drinker is more a self-identification than it is a physical condition. I would also take pain medications for surgery if I had to. I would still be a non-opiate-user from start to finish -- unless and until my intentions changed, which would require a total change of self-identity.
These are just my own impressions. I don't have any idea if there is an "official" response.
Let's see, if somebody were dangling my mother off a cliff and threatened to drop her off to her certain death if I didn't drink some alcohol right then and there, would I drink it? And would I then no longer be a non-drinker? Hmmmmmm..... Well, maybe if it were my mother-in-law, my answer would be different. Ha!