If so, will all corresponding speakers play their respective sweeping tones even though the aux cord on the AV receiver end has not been moved, as the other end is being cycled through the A16 ports?
Unfortunately, no. Measuring an existing complete surround set-up is a pain in the **s now. If the Smyth had implemented the asynchronous measurement method with sweep tones played from a disc or other medium it would have been 5 minutes childs play.
[Edit: now that I edit the post anyway because of a wrong link below: in firmware version 1.80 the asynchronous PRIR measurement method has been implemented, so if it works: problem solved!]
Or if at least the A16 could output 7.1 sweep tones as PCM over HDMI then we could at least measure 7.1 channels in one go without a problem. (And if they had implemented the special measurement mode optimised for using one or two speaker(s) we also wouldn't have to replug the cable from one A16 output to another all the time).
Even if you have an AVR with multi channel analog inputs you still may have a few problems: If it is an atmos system there generally won't be analog inputs for the height channels. (Except if the system contains seperate power amplifiers, you could go straight into those). Next problem: almost no AVR will apply the room correction dsp functions on analog inputs (and of course they will also not work when going straight into the power amplifiers).
So now what can you do? There are some possibilities:
1. Forget about copying the complete system as is, but do a manipulated measurement using the 2 front speakers for all channels (re-positioning yourself relative to the speaker). And this can be done such that you get 1 single 9.1.6 PRIR if you follow Rene Lou's recepe. (That can be adapted if you don't like his specific method of doing certain speakers while sitting outside the normal sweetspot, look for example how audiohobbit is planning to do it).
2. Replug not only the A16 output cable, but also replug the corresponding existing speakers to the front L and R speaker outputs of the AVR (but: switch room correction dsp off, or copy the settings of the corresponding channels to the front L and R channels, not possible on all AVRs).
All a lot of work, not something you would easily do in a shop unless they don't mind you fiddeling on the whole day there!
Rene's recipe:
https://www.head-fi.org/threads/smyth-research-realiser-a16.807459/page-488#post-15313315
audiohobbit's plan: [Edit: had the wrong link here, should be:
https://www.head-fi.org/threads/smyth-research-realiser-a16.807459/page-505#post-15369819]
(You can combine audiohobbit's re-positioning plan with a slight adjustment with Rene's method to get one single PRIR. audiohobbit combines measuring the front wide speakers with measuring alternative surround speakers at 120 degrees. Just skip the 120 degrees speakers and do the wide speakers only one by one if you want to create one single 9.1.6 PRIR.)