Microphones and your pedals
The first thing to note is that pedals (and processors) are designed for a certain level at the input. A proper input level is extremely important to the performance of the pedal. Effects will respond differently to variances in the input level. This can be good or bad but the impact is there and should be considered. The mics harp players use can vary greatly in their output levels and on average can be 2 to 5 times the level of a guitar pickup. Then there are volume controls on mics to consider, speaking for myself, my effects are design for the volume control to be maxed out. I had to do it this way because not all mics have volume controls.
Impedance is also very important; all effect pedals that I know of are designed with a ¼” high impedance input. Microphones vary in impedance, some are high and some are low. Usually a high impedance microphone will use a ¼” cable while a low impedance microphone will use an XLR cable. THIS IS NOT ALWAYS THE CASE, some low impedance microphones are wired to a ¼” cable causing a mismatch in impedance and a large drop in signal level. These microphones will not work properly with an effect pedal. One of the biggest issues that I see is with Shaker mics where a low impedance element is wired to a 1/4" high impedance cable and there is no matching transformer. This mic produces a very low level which works into a guitar amp but the signal is too low to drive effect pedals. A low impedance mic can be used properly with effect pedals as long as there is an impedance matching transformer between the mic and the pedal.