Would there be an advantage or disadvantage to using clarified butter to making hot sauce? Often, a recipe calls for butter to be mixed in with some pepper sauce. I'm wondering if clarified butter would give a richer taste?
Assuming you mean something like a wing-sauce when you say hot sauce (where butter is added to pepper sauce near the end of the recipe): It would make only a slight difference, and many tasters will find no flavor difference. A clarified butter is a butter with water removed---it changes the richness to some extent, but this will be mostly masked by the pepper sauce. The hotter and sharper the pepper sauce, the less the flavor of rich butter comes through.
If the recipe calls for a mild pepper sauce and large amounts of butter, then it may boost the flavor of the final sauce.
When you clarify butter, you remove the whey and casein which help emulsify the fat with the sauce. It'll taste about the same, maybe a little more 'cooked,' but it will separate much more quickly.