Is is acceptable to jump a rundown starting battery off of one of the trolling batteries in a 36V system, and can you keep the jumpers hooked up after that?
Yes, ok and common practice to temporarily jump them for emergency cranking of motor when no charger is available. Both preferably need to be of same type such as both Flooded Lead Acid or both AGM.
1st disconnect your sonar/gps transducer cable if your US2 transducer in the trolling motor is used and connected to your sonar.
You should though be jumping a cranking battery only off of the 1st or most negative 12 Volt battery of the 3 series wired trolling motor batteries just in case there is an added common ground strap between the cranking battery negative and the trolling motor negative.
You also should be using jumper cables with their alligator clamps as they help limit the max currents/heating to safe levels.
Why do you want to leave jumpers connected?