Seems like a good idea. Are the reactors still running, at low power?
Yes, the reactors are running. It's for training engineering personnel on a real naval reactor plant before they hit the fleet. I don't know what power the MTS's are capable of producing, but I doubt they are restricted to low power. The land based naval reactor training units use a water brake to be able to go to 100% power.
Reactor power follows steam demand, so I'd imagine the La Jolla and San Fran are limited to whatever the screw shaft is now connected to and how much torque it can handle.