"I'll bet the cop knows you have a CHL/CCW before he ever steps out of his vehicle. "
Nope. That is a separate computer system and they really don't care.
They don't. Here in Texas they tend to relax when they determine you have a CHL, whether you are then armed or not. CHL holders have very low rates of criminal behavior, after all they've been through a background check. Probably multiple times when they bought firearms, but at least when they applied for the CHL.