I like to imagine a Hanzo who can drink well until the others are passed out but when he reaches a certain point, he might become a totally clingy and childish drunk who latches on to the person he feels the closest to; which in this case is McCree.
I bet McCree would definitely try to get Hanzo to that tipping point so that he can see his lover acting to his true desires. Of course, he doesn’t want the archer to get angry so the cowboy would try to coax this kinda behavior only when they are in a private setting where there is only two of them.