Yeah, I wear Under Armor compression shorts beneath a pair of baggy nylon shorts, when riding.

The "chamois pad" in cycling shorts is there for padding, not absorbing sweat; any absorption is strictly incidental, and not so effective -- if you've ever changed a baby's diaper, you'll know what I mean: it just "helps" create diaper rash; same thing with cycling shorts, or any other clothing.

In fact, Under Armor compression shorts are designed to quickly wick moisture away from your skin... and they do!