Hi,
Direct mechanical vibrations can in fact cause audio noise in amplifiers because some of the internal components are somewhat sensitive to mechanical vibration. There are various components that will be more sensitive than others such as inductors and capacitors where resistors wouldnt be as affected.
But how much can this really influence the sound even with the most critical listener?
Well, if there is a component that is mildly sensitive to a given level of vibration at a given frequency, then an increase in vibration will result in an increase in audio noise, it's as simple as that. So we know for sure that there is some effect. How much effect depends on the level of vibration and the construction of the component in question. For example, if an inductor was not varnished it could easily lead to audio noise generation with mechanical vibration. Just how much however is probably too hard to determine theoretically, but a measurement would reveal a more clear picture. For most power levels i would almost be that there is usually negligible effect, but for high power levels where the speakers happen to be closer to the amplifier it's really a matter of measurement as the speaker audio pressure could cause more than acceptable movement of the amplifier enclosure. More mass would certainly help in that situation, but int he low level scenario it probably doesnt matter.
Of course a secondary factor is longevity. Vibration is often a cause of premature failure, so reduction could help a lot. If we could reduce the vibration of incandescent bulbs we could probably get more life out of them because vibration is the final straw that breaks the filament, due to a few possible vibration causes.
Class D is an interesting type of amp, because it doesnt wast nearly as much energy as any linear class. Just like a linear vs switching regulator, the Class D transistors states are all either completely on or completely off, meaning much less power wasted, while the linear class transistors are always in their linear mode. This not only lowers wasted energy, but also relaxes the capacitor size needed for good base response.
It's true that there could be lower frequency components that might be a source of noise, but they should be minimal in a good design.