That strikes me as a bit fanciful, although certainly possible and with the note that I'm not as familiar with the social status of the individuals under question as I should be. Public establishments of some sort seem to have been extremely common in Roman cities. Evidence points to them serving food of some sort and graffiti in Pompeii makes mention of multiple varieties of wine sold by the cup. Furthermore, the proliferation of small bronze change recovered from certain tabernae of Roman cities is often taken to these areas being sites of rapid small transactions in a somewhat hectic environment, pointing towards them being eateries/bars.

Incidentally, an objection will sometimes be heard that these counter top holes were not in fact receptacles for food, because how would they be cleaned?, and thus there must be a better interpretation. Luckily a particularly worldly fellow noticed that these sorts of built in holes are still common in many North African countries because when you place a ceramic bowl in them, some science happens to make them act as insulators. The Mediterranean is wonderful for cultural continuity if you know where to look.

But a simple equation of these with modern pubs is probably not wise. For one thing, they aren't terribly big, closer in size to the sort of cafes and fast food eateries common in many Mediterranean cities today than to a cozy local. For one, they seem to have been somewhat low status. The idea is that in the cramped conditions of Roman urban living there was no room for kitchens for most. The wealthy, or just in general those who could afford it, ate at home with family and friends, and those going out were only those who had no other choice. Now, I am going to go a little speculative and say that I would bet a pint on this "standard model" being heavily dependent on region. I would be greatly surprised if dining culture did not vary enormously across the empire, particularly in the northwest provinces where the pre-Roman public feasting traditions could have easily changed into a public dining culture. Absolutely no evidence to my knowledge, but I would have difficulty believing the "standard model" actually held true across the Empire.

So the short answer is that it was certainly possible, but perhaps not in keeping with cultural norms. They probably shared their drink at one of their houses. A great depiction of the "standard model" of Roman dining is in Mary Beard's Fires of Vesuvius--a limited topic but most of our evidence comes from Pompeii anyway.

Generally, wealthier Romans drank their wine at banquets, called conviviums. At these banquets, each drinker would get their own wines, depending on their social class. These were largely social occasions, where politics would be hashed out. Unfortunately, I can't find any more information, and I'm not sure if there were bars for peasants.

Source: A history of the world in six glasses by Tom Standage