It's my understanding that the purpose of the hose running to the stuffing box is not cooling or lubrication. Stainless steel in the absense of oxygen will corrode. Salt water has disolved oxygen but over time the oxgen gets depleted in the deep dark confines of the stuffing box and shaft log. If you do not replace the saltwater then over time your stainless steel propeller shaft will corrode quite badly. You would think stainless steel is rust proof tough stuff but I have actually seen some prop shafts come out of boats all pitted/corroded to the point they had to be replaced. Remember it's Stain Less
While motoring your raw water pump, pumps salt water through your heat exchanger. About 90% of that water ends up in the exhaust. The remaining 10% is fed out of the heat exchanger
through a siphon break at least 2 feet above the waterline and then back to the stuffing box/shaft log. That 10% flushes out the oxygen depleted water and any marine growth in your shaft log. As far as cooling I doubt it does much of that considering your engine runs at 180 degree F and I'm sure the water coming out of the heat exchanger is at over 100F. I installed a bronze sight glass with a paddle wheel in the line that goes back to my shaft log. At idle I don't see any water passing by but under load I do see the water trickle by.
Scott s/v Magnus