If the singer can calmly do a good performance without hewarin the effects just record the clean sigfnal & then afterwards send which track out to a Reamp box then to the effect box then to a DI then to a mic level input.
If they need the effects in real time ( watch out for stomp box switch clicks into the mics ) Nevertheless you can do something similar. safely using a Y cable or hypothetically patch bay may or may not manually work because the difference of impendence between the mic pre output and stomp box input. What's you mixer situation? To all intents and purposes run the mic pre out into one channel and then use an effects send out to a Reamp box to the stomp box to a DI to a mic input.
There are also cheap passive mic line level splittrers you could use atlkhough
I haven't tried this one it's cheap :
http://www.grandmas.com/ItemArtSplitCOM.html
I'm sure there are other ways to do this too.
Presently best of luck!