Each electronic component produces some dirt, be it EMI, RFI or a ripple on the ground plane.
You can’t rule that e.g. a ripple on the ground plane modulates the analog out of your DAC.
In the past this was a problem. On my old Toshiba laptop I could easily measure the difference between running on AC or DC (yep, the latter makes things worse!).
Today this is less of a problem, noise control is better.
Now if we apply this to your situation the question is will using different interfaces (local HD, external HD, Network interface) produces such a different noise pattern that it will become audible?
Personally I do think this not very likely.
I have fooled around with all three without noticing any difference.
But I do use an outboard DAC over Toslink so it is galvanic isolated from the PC by design.
YMMV as they say.
Best is to run a little experiment yourself.
Try local HD, a USB thumb, whatever you have at your disposal.