Haven't really try that before, but I would believe that should be the case. As I would believe the "noise" of the HDD, the concern is not really about the noise that you can hear, but the electric noise that the motor generated which will pollute the audio signal.
On the other hand, if you use SSD, you'll feel better as your PC surely run much faster.
I am Squeezebox user. I store FLAC in PC which is located in bedroom, and I play music in the dinning room.
I just wonder will there be impact to sound quality for this setting:
(7x24 PC) -> Ethernet -> SB -> ...
I don't use special power cord and power supply for that PC, and I don't use SSD for storing music files too.