It won't. The whole point of a balanced connection is not that it does't have ground noise, it is that it doesn't care. The noise is added equally to the hot and cold signals then when they are subtracted from one another at the input to your amp, it cancels out.
But the noise is carried from the one device to the next IF signal GND is also connected to the shield. Noise put on the signal wires wil be canceled out. But the way the ground seems to be connected noise on the shield will be transferred to signal ground.
If, eventually all connections become balanced, this should indeed solve the problem. But as long as the connection to the speaker-amp is SE I'm not certain.
Then that is unlikely to be the noise source. Unless noise is going from it to the mains socket, and then from there backup through the DAC and down the analogue interconnect to your sub/amp earth connections.
When the sub is removed from the chain, there is no digital noise. So I think it's the signal ground that is picking it up trough the RCA cable. Either the one running from the sub to the speaker amp or the one from the DAC to the sub.
When I had the DAC connected to the speaker amp directly there was no audible noise from the PC. The cables were much shorter (further away from the PC) and higher quality.
I'm thinking about running the "long" RCA cable from the DAC to the speaker amp, next to the PC, removing the sub from the equation. Just to hear if it is the cable.
I suspect that it is the sub or the cable connecting the sub to the speaker amp, since I don't think there is any noise coming out of the sub itself. (need to check that again)
(I'm assuming the noise is ground noise at the moment)
I think so too. Somewhere picked up by the signal ground going from sub(-amp) to the speaker amp. But like I said, signal- and chassis-ground and shield seem to be all connected, which I think creates the problem when using SE connections.