I am particularly interested in understanding the relevance (or lack thereof) of having the nitrogen generator on for extended periods while the ion source of our MS/MS is deactivated or idle.
As a consultant who trains people in the operation and servicing of these systems, my answer would depend on the type of source, configuration, make and model of instrument. Are you asking about the desolvation gas (some vendor's refer to it as the 'curtain gas' or nebulizer gas, but others do not, so check its function to be sure)? This is the gas that mixes with your mobile phase and is introduced into the MS. That gas can be safely be turned down or 'off' on many instruments when they are running in a true standby mode. The definitions vary by manufacturer. You will want to contact the manufacturer of your specific instrument for advice. On some systems, the Nitrogen gas is needed for cooling and temperature stability while the vacuum pumps are 'ON'.
Proper procedures for running, fully shutting down and placing the system in a warm stand-by mode should be well documented in your SOP's and Instrument log. Most systems run all of the time, never being fully shut down unless a full source cleaning is needed or the system will not be needed for one month or more. Operator training usually includes these important procedures (We like to have them written down in a book kept near the instrument). Trying to save some energy and/or gas may lead to very expensive instrument failures, so when in doubt, always contact the instrument manufacturer for specific recommendation as to which areas you can safely conserve gas or energy without compromising instrument function.
Our (AB SCIEX API4000) system uses curtain, source and exhaust gases generated by a PEAK nitrogen generator. I was actually contemplating deactivating the turboV source (ESI probe) to reduce the demand for gases from the generator. The generator needs servicing which cannot be performed before before a couple of days.
To think about it, the nitrogen generator is sometimes off for up to a week whenever there is a delay in servicing by the engineer. I have never really noticed any adverse effects on the MS/MS when it was eventually brought back online.