Even if you haven’t seen The Curse of The Were-Rabbit. There’s a villain character who snarks that the paranoid vicar going on about a were-rabbit is because “he’s been to the communion wine again”. I’ve seen a few descriptions saying this implies he’s an alcoholic, and I can see that because “again” means there has been a wine situation at least once.
I’d say it’s more snark than implied alcoholism.
It certainly could be said in cases where the vicar is known/suspected to have a drinking problem, but it could just as easily be said, with no prior basis in fact, as a dig at someone, meant either nastily or humourously.
The fact that it’s a well-known phrase (including the “again” part) makes it all the more likely that it might be used even in cases where there’s no intended implication of a genuine drinking issue.