Yes, the motor is totally isolated between R & L water jackets and the coolant only mixes in the radiator tanks. That's why it's a good idea to use dual temp gauges.
The side that doesn't have a thermostat will mostlikley overheat and crack the block. The Flathead needs a lower rate of water circulation than the water pumps produce to insure proper cooling, the thermostat provides the correct rate.
I use nothing but 180's and Ive had no problems in mid 90's summer beach traffic and parades. Be sure the block & head water passages are clean, radiator core is good and timing is on the mark. Use NGK B6L plugs.