Mics output low Z signal and guitars output Hi Z.

SO running a mic into a distortion pedal is not a good idea.

You can stick FX processors over vocals buy using the insert points of Fx send and returns on a desk. This will bring the mics lowZ signal up to line level.

Some bits of kit are made to plug directly into a microphone.

You may be better checking out something like a Digitech Vocal processor . I had one and it is OK. There is also a newer more expencive version here . I think the differences is that the latter also has a USB port.

A guitar stomp box can be used in conjunction with a desk however the impedance will be mismatched which will mean the sound quality is sub-optimal.