Is it possible to connect a microphone to an iPhone/iPad via WiFi and use it instead of the built in one?
it is possible to do it through bluetooth, dock connector, and 3.5mm headphone jack!

in order to use it though wifi you need a compatible application and i have never heard of such thing! after a little goggling all i found was bluetooth connected ones, because it offers a P2P connection witch is much more reliable!

(sidenote) mics though wifi routers could, be unreliable, specially in poor connection!

however there are mic's that include a dock connector dongle for a stable P2P connection 
something like this