Ground loop hum would not go away as you describe. You don't have ground loop hum. You have another problem. And your question about the interconnect is complicated.
All components even with just two plugs are grounded. It is not a Murphy, it is just the way electrical panels are wired. Black is power, white is neutral, or utility ground. Millions of homes and older appliances wired this way, perfectly safe. The third plug is earth ground, redundant since neutral is already ground.
Vast majority of components every speaker output and RCA in and out, they are all grounded to the same chassis ground. Look inside, all the RCA are wired together. Ditto speaker terminals. Since this is the same on both components then yes connecting them with the interconnects connects the grounds and if one is earth grounded (third prong) then both are.
Where it gets complicated is the whole point of that redundant extra earth ground (third plug) is extra safety, which in order to work it needs to be able to carry a lot of current. Which is why the ground wire is always the same gauge as current. Not so the interconnect. So yes it is grounded, but no it isn't. If you think this correct answer is hard to understand, just wait till you see how thoroughly messed up it gets from here. Electricity questions are just the worst! Makes me want to bang my head into a Max Headroom sign.