dmankin wrote:My question is this; Should a properly functioning rotary pump be silent, near silent, or make a whirring sound?
Vibratory pumps get a bad rap because... they vibrate. If you run one free from an espresso machine's casing, it makes less noise than an electric razor. Alas vibratory pumps do indeed vibrate, producing a tinny reverberation of interior components. I'm not making this up, I "outboarded" mine and the noise level is about the same as an inboard rotary pump:

Rotary pumps by their nature produce very little vibration. If they have an ample water supply to avoid cavitating, they operate nearly silently. If they're mounted externally as is the case in the majority of cafes, you will hear nothing unless you open the cabinet and listen carefully. Most manufacturers of inboard rotary pump espresso machines mount them on squishy rubber footings, arresting the little vibration the pump produces.
I
assume the whirring sound you hear is not from the pump itself, but sound produced by sympathetic vibration. Mounts that are made of too hard a rubber, not enough rubber, components touching each other, etc. can result in odd buzzing that is very difficult to locate. As a case in point, the original La Spaziale S1 rotary pump mounts were replaced by slightly softer rubber in the final production model. I retrofitted them in during the final weeks of testing and was astounded by the noise level reduction. So the answer to your question "Should a properly functioning rotary pump be silent, near silent, or make a whirring sound?" is regrettably "it depends."