Have no fear, Exodus is here. haha. Okay, anyways, I busted the same hose, only while I was driving. Not pretty. It's the water inlet hose for the heater. the one on the passenger side that that connects to the head under the coil right?

It's number 2 on the diagram. Honda wanted $18 for the hose. I said f*ck that, and went to Kragen. They had a generic hose that fit the application, for $6. Basically a molded hose with a 90 degree bend.
Yes the leak will cause the car to overheat, especially at idle. Whenever your coolant level drops a significant amount, the car will start to overheat and you'll get the fan turning on after the car shuts off. It's like a polite reminder that you need some water/coolant, haha.