You could possibly get a mic level signal to cause it to trigger, but the unit is made to work with line level signals really.
If you ran the mic to a preamp first, then the preamp out to the D4, that would be ideal. You will probably want to have a noise gate between the preamp out and the D4 input to help alleviate false triggers though.
Ideally, the best way I have used the D4 for triggering is to record a drum track, edit out all background noise on the track in a DAW, and feed that editing track to the D4. This way, I can MAKE SURE that NOTHING but the drum hits I want trigger the module.
Ed