I do refrigerate my fondant covered cakes without any problems. If they have any condensation , don’t touch it or it will leave marks. Before I had a steamer that was how I got rid of powdered sugar marks.
I’ll second that… I refrigerate mine all the time. They will have some condensation when they come out of the cooler. Let them sit and it will dry back out. If the condensation bothers or worries you, you can always put a trash bag over the cake (taping the “top” of the bag to the sides of your cake board) and it will prevent the condensation all together.