I don't think Quark would be required to give it for free, he'd just have to deal with people who never have money and expect things for free who would think he's strange for charging money and go some place else instead (this is assuming a currency free Federation as opposed to the idea of one where they do have money, it's just that the pursuit of wealth isn't desired).
Quark complained at several points throughout the series that Federation membership for Bajor would mean the end of his business on DS9. I would assume that would only be due to the lack of an ability to make a conventional profit as there are obviously proviately owned businesses within the Federation.