Without predicting what the failure mode of a dead battery will be in the future, I cannot hazard a guess as to what the results will be.
If in a lake right near the marina, go ahead and give it a try. If 50 miles offshore, on a stormy day, when it is getting dark, I would first try starting the motor on the house battery only and then parallel the two batteries once the motor is running, to see what happens. If the motor runs well, fine and good. If the motor starts to run poorly, or worse dies, I would personally run home on the one good battery.