Yes, actually. In my experience they're more likely to support you, and to pay extra, if the base price is zero.
People very rarely comment (ratings are more common), but they often add games to collections. And I don't remember numbers, but the old rule of thumb from publishing (and commerce in general) applies: maybe one in ten people will check out your game. Maybe one in a hundred will get it. Maybe one in a thousand will offer any feedback. Don't get your hopes too high no matter your price policy.