“The Mishna Berurah writes that many places have the minhag to duchan on Simchas Torah by Shacharis (or not at all) because the Kohanim may be drunk”
A Reviis of wine is enough to passul a kohen from going to duchan. Perhaps the mishna berurah simply means the minhag is to duchan by shachris because many kohanim would have made kiddush and had a reviis of wine by the time mussaf comes along. That is how my Rav interprets the mishne brurah (some bachurim wanted to bring a proof from this mishne brurah that getting drunk on simchas torah is endorsed by the mishne brura and wanted the Rav to relinquish the keys to the closet where the liquor was kept).