First, yes! As long as your cake is completely covered with buttercream or ganache, you can fridge it just in the cake carrier, as the frosting/ganache seals the cake and keeps it moist. And I’d say, if you have a very fluffy frosting or really precise piping, this might be the way to go.
However, at the same time, buttercream and most ganaches are pretty solid in the fridge, so if you don’t apply pressure to them, they can handle plastic wrap. The idea is to sort of protect the cake from the air in the cake carrier—although I’m not even sure if it’s really a problem. However, I wrap anyway.
This is what I do: I put the cake on the cake carrier. Then I take a piece of plastic wrap about 14” long and start it about 2” outside the cake carrier, along the floor of the carrier, up the cake, and let the rest lay on top (and some might do down the other side). Then I do it again until the whole cake is covered. The idea is to pretend the cake has sunburn, so you are draping it gently. Then you can sort of pat teh whole thing so all the plastic wrap sticks to itself and the parts that hang off the carrier help to seal the air within the carrier from the cake.
Usually, it can be lifted off like a big hat before bringing the cake to room temp.
I’ve only done piping a couple of times—with neoclassic—and I’ve never had a decoration marred. And for “regularly” frosted cakes, the surface wasn’t marred at all.
Good luck, whichever route you go .... and if this is with respect to an actual, rather than theoretical cake, post pics!!!