set up -- does TC fluid actually mix with the pan fluid in some fashion while operating?
Absolutely! The fluid is pumped into the TC, and from there circulates through the rest of the tranny before draining into the pan.
Is draining/refilling a time or two a close enough approach to cleaning out the TC?
Yes. The normal service interval (whatever that is) is supposed to take this dilution of new/old into account. Unless something is wrong and the fluid is being ruined early. -- Jim