Yes your theory and concept is correct. However, do be warned that an audio ground loop isolator transformer usually do not respond/pass through flat to low frequencies, IE Subsonic ones, unless they are absurdly expensive. For the normal ones, the lower end of the frequencies will be at a much weaker volume than the audio frequencies higher up at 40-80Hz. IE the 15-25Hz, the LFE range may be at 1/4 volume or less while a 50Hz tone will go through the transformer at full volume.
Verify the quality of your RCA cable's GND coax. Make sure it is a really thick good quality braided copper. The frame ground connection you have may also help. Unless you are willing to pay for an ground isolation transformer which operates flat below 20Hz, it may be advantageous to verify if you can fix your hum issue without the transformer.
Also, I've see some isolation transformers incorrectly internally wired which invert the amplitude phase of the audio going through. For a sub-woofer which you want firing outward on a (for example) explosion in a movie you are watching, such an incorrectly wired transformer will make the sub-woofer fire inward instead of outward. I would not expect this issue with an expensive ground isolator which was designed for very low frequencies.