Ya need to hold off on your "life savers" comment for a little while, we ain't there yet.
You can start and run the engine for a short time without cooling; most say about a minute, my small experience indicates the thru-hull seal for the drive shaft gets very warm after about 30 seconds. However, if you managed to run for a while before having the problem on the water, you will probably not have enough time in the back yard. Would not hurt, just for the exercise of exercising the fuel selector, to give it a quick test on reserve or leave it on reserve for next water test.
I have gone through the electronic schematic and do not see any feedback into the electronics from the overtemp sensor. If you were a techno-geek like me you would hook an ohmmeter across the temperature sensor and put it in one of your favorite lady's small pots with a thermometer and water; resistance should drop to about 0 at about 200 degrees f. If this proves true it would sound like an actual overtemp problem and the necessity of going thru all the cooling lines; quick test would be in the water where you should get some flow out of the "pee holes" on the back of the seat pedistal at about the level of the deck. I cannot figure how this would shut down the engine except for the bad situation of seizing up.
Almost to the point where one of the experts may need to bail me out here.
But we are having fun, correct?