[1] Summarising, I am assuming when dealing with one or a small number of ADCs you will have no benefits in using Cesium/Rubidium clocks.
When dealing with a certain amount of clock recovered equipments there is need if not must for such external references.
[2] Now remains the question of audibility of those issues as per nick_Charles's post.
1. Starting about 20 years ago, there was a big thing in the pro audio community about external clocking, largely due to the misleading marketing claims by one of the most respected high-end manufacturers of pro ADCs at the time. The whole thing culminated into probably the most infamous public argument in the history of the pro audio community, as it was extremely acrimonious and involved a considerable number of the biggest/most influential names in the business (Bob Katz, Bob Ohlsson, Dan Lavry, Nika Aldrich and a whole slew of others). That aside, here are the basic rules of studio/pro clocking:
Regardless of how good/expensive, an external clock will not improve the performance of a pro ADC. An external clock will degrade the performance of an ADC or in the very best case scenario not make any difference. When linking digital audio equipment together (say more than one ADC, a digital mixer, etc.), a master-clock source is absolutely required, otherwise the system simply won't work. In general, the best source for this distributed master-clock would again be the internal clock of the ADC. There are some exceptions however, some complex studio topologies and most scenarios where audio and video require synchronisation for example. In these cases an external master-clock maybe beneficial or even unavoidable but even so, there is no advantage with those ridiculously expensive clocks over far cheaper alternatives because the clock signals they produce are never directly used by ADCs. Even in this scenario, the ADC is still using it's internal clock, which in effect is regenerating the external clock source. The determining factor is the quality of the clock recovery/regeneration topology of the ADC not the accuracy of the external clock. A decent $200 external master-clock will end up with a regenerated clock signal in the ADC which is no less (or more) accurate than if the external master-clock were a $10k+ atomic clock!
2. The only published study figures I've seen, indicates a threshold of audibility (with music material rather than test signals) of 20ns. I can't remember where I saw it though and I also believe it's been disputed (claiming the figure should be significantly higher). Even accepting this 20ns figure as the audibility threshold, that's still several hundred times more jitter than modern pro ADCs produce!
Yes clocking is very important as that was drilled into my head by Mr. Ludwig and Mr. Williams about 20 years ago to use an external clock.
Oh dear! Are you really claiming to have been taught by the legendary mastering engineer Bob Ludwig? If so, I'm going to call you out on that lie too! Bob Ludwig knows his stuff and while I can't quote him directly, I can quote him indirectly (from another legendary mastering engineer, Bob Ohlsson) from over a dozen years ago:
"
Bob Ludwig made it very clear during his workshop the other day at AES that what sounds best to him in his room is using the internal clock of an A to D and, for playback only, clocking the entire system off the internal clock of the D to A converter. He spoke very highly of using the Big Ben for locking to video but never suggested he uses it in place of an internal clock when that's possible."
It's not plausible that you even have a college level education in digital audio, let alone be personally "drilled" by one of the industry's greats. Why do you persist in these lies, especially such obvious lies? I can't see how being exposed as a persistent liar is of any benefit to you and your lies are certainly of no benefit to anyone here, so for you own (and everyone else's) sake, please STOP!
G