Jeff Volek found that low carb athletes maintained the same muscle glycogen levels (use and repletion) as high carb athletes while having a 2.3x greater level of fat oxidation. So we apparently prioritize repletion of muscle glycogen even when we are making the glucose from scratch and are otherwise glucose sparing.
That implies in both cases (carb burner and fat burner) the body would push glucose into muscle cells which would lower glucose levels and require more to be made. I’m not sure if the same is true for liver glycogen above the immediate requirements for the brain.
We often hear that protein isn’t stored, but about 1% of the protein in our body is labile - that is it’s being used for optional purposes that can easily be re-tasked. Another thing we can do in the short term is scavenge urea from the blood and make non-essential amino acids from scratch (de-novo genesis) - so there is some elasticity in supply. I suspect there wouldn’t necessarily be an immediate debt come due, but you would have to increase your intake of protein afterwards to repay that debt.