Can you connect a mic into a guitar multi effect processor without damaging anything? Can you get some decent vocal effects that way or will it sound like crap like connecting a mic to an amps guitar input?

Dont expect anything drastic,but its fun to fuck around with.It should not damage anything,as long as your not trying to wedge those 3 prong microphone chords into it,make sure its a 1/4 plug.

Won't there be impedance differences? My mic is KSM27 and it has 150 Ohm output. I don't know how much impedance output multi effect processors are.

Im not sure,but I can say that I have done it before,and it didnt fuck anything up. But dont hold me to it.