Maybe. But by no means guaranteed. Low(er) rails derived from the main output rails, will usually have their own decoupling caps, and if they are derived via monolithic regs of the 78 / 79xx series, then the typical ripple rejection of some 80dB that these devices have, will pretty much knock any ripple on the head, before you even start counting in downstream decoupling caps. Thus, my point, that you could have a DC fault giving rise to dirty 'raw' rails fed directly to the power amps, whilst still maintaining clean low rails to the preamps, in which case, the volume control will have little or no effect on the hum.
Anyway, this is just becoming a worthless discussion of perhaps's, maybe's and diagnostic experience, as Jak suggests below. I can only contribute suggestions based on what 30 odd years of repairing this stuff on a daily basis, has taught me about faults like this.
Arfa