Funny you should say that. That is exactly what they did with Michael Ansara's mustache when he played Kang in "Day of the Dove."
Ansara seemed to rock some pretty serious 'stash when seen elsewhere so I'm not so sure...
From this HD screenshot it sure looks like the whole thing is stuck on. It has some pretty sparse areas like an appliance, and it's uneven with some pretty hard edges of where it ends on his upper lip.
Oh, man, that's obviously a fake mustache. The tape on the left-hand side even overlaps his philtrum, and it's so blatantly squared-off.