Some good points BUT He has servants to do all the things like shave Him and stitch His arms back if a Zombie, A bit like in the the Movie Death Becomes Her ....
...and if He is working as a Human He could simulate being drunk to play the part to disguise the fact He is a Vampire.......
...also we have to consider that maybe the Vampires from CJ were used to alcoholic drinks ands Vetinari is not.... I know people who can either drink all night or fall down after a quick half so we can't assume that He is not a Vampire because He gets a little pished!