With daily consumption of wine estimated to be about 1 liter/day based on production, vitamin c requirements may be about covered. Was that a reason why these enormous consumption levels were thought to be healthy, despite some side-effects that would not have escaped the medics of the time?
Wine has no vitamin C at all, so the answer would be: definitely no. But there's a twist.
To expand on @LarsBosteen's comment: the wiki page on Posca and romae-vitam.com claim that Posca, rather than wine, actually may have been the antiscorbutic the larger population relied on. It's basically a mix of wine vinegar, water, and additives thrown in for flavor (Romans, as an aside, thought of drinking wine pure as vulgar). That is a lot more plausible - especially given the recipe suggestion on romae-vitam.com:
- 1.5 cups of red wine vinegar.
- 0.5 cups of honey.
- 1 tablespoon of crushed coriander seed.
- 4 cups of water.
(Keep in mind that this is a recreation, as it seems we don't actually know for sure how Romans would season Posca exactly. Honey in particular was expensive enough that I sincerely doubt your typical peasant would use some to make Posca.)
At any rate, coriander seeds have ~21mg of vitamin C per 100g. That pales to kale (120mg) or lemon (53mg) but it's a lot more than in olives (0.9mg), honey (.5mg), or red wine vinegar (0mg).
I'd surmise their vitamin C requirements were met by fruits and veggies first and foremost, but during a winter campaign abroad, drinking Posca following the above recipe could seem like a good enough source - with the caveat that it's the seasoning, rather than the wine or the wine vinegar itself, that is providing the antiscorbutic properties.