Yes, coolant does run through the throttle body. If coolant is leaking from the gasket between the plastic UIM and the metal throttle body, you should be able to replace the gasket and call it a day. The other possibility is that the plastic of the UIM has degraded and is starting to fail, in which case you would notice signs of that, and should be on the lookout for it. If the plastic is cracked or failing, the UIM should be replaced, and the LIM gaskets with it.
I also had the top radiator hose dripping on the exhaust crossover at one point, and it took me a while to track that down.
My UIM did fail on the PA, but mine was leaking from between the LIM and UIM. If the throttle body gasket is failing however, you do run the risk of ingesting coolant which can go very badly very quickly.