Well, after a day on 2 tbsp red wine/gallon of water for my chickens, here is my report:
When I checked them around 2pm, there was no noticeable difference in behavior.
When I checked them shortly before dusk, I thought they seemed especially lively for a frigid November afternoon, but I can't tell for sure that that was the wine. I mean, they weren't singing or dancing or anything.
The French thread seems to indicate that the wine helps with egg laying. Seems silly, but hey, who knows? It would take more than a day for that to show, though, so I might keep it going for a few days.