All the Hondas I've known, the thermostat is at the LOWER radiator hose. The hot water comes out from the engine, mixes with the cooler water coming back from the radiator, and the T-stat measures it there. From the T-stat, the water goes thru that pipe into the suction side of the pump.

But anyway, if the water pump isn't working, or there's substantial air pockets, then the water isn't circulating properly. In that case the thermostat doesn't see a good representative temperature so it IS a problem.