I don't think they do, or at least not very broadly and holistically. Cycling research budgets just aren't all that huge; optimizing particular components for particular properties is a thing, and characterizing what's optimal is done for a few things where there's an efficient and repeatable way to measure effects with fast turnaround. Less so with things that are messy and take time to measure... even things that have demonstrably significant effects. For instance, suspension is the entire reason that we use pneumatic tires, but it's only been the last decade or so that anyone has gotten around to actually characterizing that effect on road bikes.

Maybe. Or maybe not. Probably not much, if that talk Abe_Froman linked is anything to go by.