Yeah, that's possible.
You are going out of your way to make a very simple thing very complicated.
I know you are not doing it on purpose and your questions are sincere, but I suggest you drop back and reflect on how simple your desired outcome is and find a simple solution to get there.
If you really want to switch a mic signal in a floor box we'll have to start talking about buffer amps, relay switches, power supplies, and... etc.
You can get a passive mic splitter... but a mic switcher will make noise if you don't have all that other stuff I started to babble about.
If you really want to switch a mic signal in a floor box then I suggest you shop for one of the very few vocal stomp boxes that are out there. Some of them have really cool effects built in.
I've seen a few, I imagine most of them that I am aware of have been discontinued due to a lack of interest in the market.
If you really wish to go that route then you'll want to search out the latest, greatest version of a vocal stomp box and try it for your self.
I recommend that you choose a simple solution.
best regards,
mike