good question, as long as your cake remains at 32oF, the buttercream is rock hard, so no plastic wrap marks. But if it becomes warmer, thus softer, there will be marks! Most refrigerators are as warm as 42oF, you will need to test this; read the temperature of your buttercream, once it has reached 32oF remove the wrappings.
Plan accordingly, you really DON’T need nor want to smooth it out again. Buttercream is best worked when at room temperature and freshly whipped or re-whipped, otherwise you get bubbles.
If your cake isn’t big, you can use a plastic cake container instead, this will be worry free. Except, there will be ice build up on the air spaces of the cake container and a little too on the cake itself! You will need to somehow close the container on a non humid day?
It is impractical for me, as my cakes tend to be larger and odd shapes, plus cake containers take so much room from the fridge.
By all takes, NEVER leave cake exposed in the refrigerator (or freezer) for more than 2 hours, as buttercream will absorb your refrigerator odors. BTW, my refrigerator and freezer are completely odor free as everything is vacuum packed, and I never let anyone put any left over foods unless well sealed!