It would if it were vented overboard. My understanding is that the waste heat from the exhaust is used to flash the LOX to gas so it can be mixed with the fuel and burned. The cooled exhaust is compressed and stored in high pressure cylinders and vented at the end of the mission.
Doubtless someone will be along shortly to correct me if my understanding is flawed...
The LOX is just expanded to gas and mixed with diesel in the Sterling engines. I guess just the gas pipes need some heating to prevent ice. The carbon dioxide exhaust is dissolved into the seawater without bubbles.