I am making kitchen cakes for a graduation dinner to supplement the tiered centerpiece cake. I am currently baking and freezing all the layers. I plan to assemble early the day of the graduation. All fillings are stable, but I will be frosting with RLB silk meringue buttercream ( an IBC variant). I will tort, fill, crumb coat, weight and settle in the morning. After final frosting, is it OK to refrigerate for several hours? Does refrigeration for a few hours affect the texture of the cake? Or will the buttercream be OK at room temp for several hours? Thanks in advance

Can't answer the fridge question, but IMO, you need to back up that timeline. Settling occurs best if done overnight. For best results I allow 10-12 hours. 2 is an absolute minimum.
And you should always have a cake finished the night before delivery, just to provide some "safety" time if something goes wrong. I definitely would NOT be icing even a kitchen cake the morning of the event.