Such a coin has been found. The numismatists describing the find list three possible causes: 1) Unofficial issue, either as a counterfeit, a novelty item, or for use by an unscrupulous gambler. 2) Mint error 3) Purposeful mint issue, such as a commemorative medallion.
Could have sworn I saw something like this at a recent auction, with Constantine's mug on both sides but different legends. Can't seem to find it now. Still a really cool and intriguing issue. If the portrait die was the free one, perhaps someone managed to steal two obverse dies from the trash and mint a coin with them? I once found a two headed nickel in my change and almost didn't even notice because how often do you check both sides of your change? I am sure the ancients were no different.
