I would not, because it could sweat when it comes out.....its not necessary
I don't think so.
I refridgerated a cake with mmf accents and when I took it out all the peices started to melt as they came to room temp. I learned the hard way.
Beth 
Would fondant stay on creamcheese icing and would it have to be refridgerated?
Fondant will stay on cream cheese icing if it's already a stable recipe (in other words, I just read a few posts from people with sliding cream cheese icing...obviously it won't stay on if the icing is already sliding!!) but whether or not it must be kept refrigerated depends on the recipe. There are shelf-stable cc icing recipes around - including one on earlenescakes dot com.
If you refrigerate a mmf cake just be sure it's not sealed up in anything as you want the air to circulate around it. You can take it out and just let it sweat, just don't touch it, and try to get it near a fan or something to help blow the air away to keep it from condensing on the cake. I did a christening cake in mmf and refrigerated it - it sweat but then was fine although I put the decorations on it AFTER taking it out of the fridge. Hm, I have a little white dragonfly/flowers cake that was also mmf and refrigerated with no issues, and that was WITH the green fondant ropes and gumpaste flowers on it.
If my icing/filling doesn't need to be refrigerated though, then I prefer to not refrigerate mmf because I'd rather avoid the sweating.
I now use the Michele Foster's fondant recipe because it refrigerates with NO issues whatsoever. You can also look up MacsMom's MMF recipe, as she said that she ALWAYS refrigerates - and her cakes are fondant works of art! I think she adds glycerin...perhaps that's the magic ingredient to eliminate refrigeration issues...?
Like Ceshell, I too use MFF (not marshmallow based at all), but used to to MMF. Refrigeration does nothing to a fondant covered cake. Take it out, don't touch it, don't try to mop up condensation, and in no time, it will be smooth and matte again like it was never in there. A fan can speed things along.
Further to what Jamie just said, the real problem is if the condensation can't evaporate (and since it's generally rather dry in your fridge, the condensation doesn't even form there, it's when you take it out. Cold cake meets air = condensation forms.
My MMF disaster occurred when I refrigerated cupcakes with MMF decorations....IN a tuppeware. The moisture had nowhere to go but back into the fondant, and the colors ran and bled like you wouldn't believe. Fortunately, they were leftovers!
I don't even think refrigeration has that much to do with it - it just creates a self contained environment to trap condensation (like a terrarium). I also foolishly put UNREFRIGERATED cupcakes with fondant decorations into an tupperware. Nice, moist cuppies...fondant decorations...airtight container...can you guess what happened? 
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