Yes! You can completely frost the cake and keep it in your fridge. It will be perfect on Saturday night. In fact, it will probably be moister than if you served it immediately! The frosting will “seal in” the freshness provided there are no gaps between the frosting and the platform the cake is on (and no other exposed cake, of course). If you don’t have a cake carrier to cover the composed cake completely, once the cake is firm from the fridge, seal it to your platform/carrier with plastic wrap to help keep out odors (although I’ve never had this problem).
Remove the plastic wrap while the cake is still cold so you don’t mar the frosting.
Give it a good 6 hours to come to room temp. if you can’t do that, you can at least be content that, once it’s cut, it comes to room temp more quickly. You can always cut cold slices and then they only take about 20 minutes to be completely soft.
I would let the frozen layers thaw in the fridge overnight—or at least thaw some, somehow (even wrapped, on the counter, for an hour or so)—before frosting so that it doesn’t expand in its frosted state and cause splits.