In some cases it will. It never hurts to ground the cable at the service panel. Any difference in potential on the safety grounds at your equipment can cause a hum.If I understand the root cause of ground loop hums, this seems like it will remove the voltage potential that is causing the hum.
Even though the safety ground is a cold conductor, it can and usually does, develop a small potential, through mutual inductance, wire resistance and various other reasons that can be quite different at each receptacle in your house.
When you plug a power amp into one receptacle and a preamp into another receptacle, the metal cases of these two units can have a small potential difference in their safety grounds which means that this equipment's metal cases are at a slightly different potential. When you connect a single ended (RCA) cable between these two devices, a small AC current can flow in the shield because of the potential difference. This unwanted signal is in the signal loop circuit and can cause a hum. An interconnect circuit has a loop path (completed circuit) that flows through the centre conductor of the interconnect cable and back on the shield. If there is an AC signal on the shield flowing because of the ground difference potential, you'll hear a hum. Breaking the safety ground of one of the two devices removes the potential and the path for the unwanted signal flow...
Exactly the same situation can occur, except usually worse, when you introduce a new ground into the system from cable TV or a satellite. Their ground on the shield may possess a different potential than the ground in your system and current will flow in all the interconnects. Usually by centralizing and bonding all external grounds to the common house ground you're at least giving yourself the best chance of reducing this problem.
With cable, sometimes it's necessary to use an isolator device like this one. They usually work - not by magic, but by using an RF balun or similar device. They are quite safe, albeit a bit expensive.