hi,
I would say this is still binary data regardless of whether you code it "yes" and " no" or 2 and 0 . As such, calculating averages is strictly speaking meaningless. E.g. if you code differently, like yes=10 no=0 you would get probably very different results, and your test must be independent of the way sou code.So, i would say, you have to treat those as discrete, binary data and use the proportions test.
regards
rogojel