I think it’s nice that you are sharing your expertise in optics, however, from a hands-on experienced perspective, there are several issues you are not addressing. Then when I scrolled down to see you were using an SCT, this sheds even further issue into the matter. Is there anything you would like to add regarding off axis placement before I say anything?
Hi, Daniel; Wax lyrical, please!
My intent was to only and briefly answer the topic-starter guy's fundamental question, with a 16-inch Newt as an example... and then later show a different example of fiddling with variable mask to scrutinize the sources I had designed and built for a test-lab collimator. My use of the word ~differential astigmatism~, in the Newt example is paramount there. All he wanted to know was if the longitudinal placement of an off-axis stop (on the object-space side of the system) changes things much --- and the answer remains resoundingly "No.", regardless of the configuration of the telescope. That is, stop at entrance port vs stop at first significantly-powered element... will not noticeably change the effect of stop / no stop. What mostly changes is the stopped-down enlarged Airy Disc... little else. I didn't want to mushroom that into a detailed theoretical discussion --- at least for the basic question.
PS: Geometric Spot Diagrams are great, but the full-blown coherent solve is where the action's at, for off-axis stops. Thankfully, we can generate those quite nicely now-a-days. The off-axis-stop impact is almost entirely diffractive.
[My career was building imaging satellites, including Hubble-class and even more ambitious. I was frequently in friendly battles with the Systems Engineers, who would (understandably) analyze the bejesus out of every concept... but frequently present the shops with unbuildable designs. So, we would bounce back and forth, until we wound up with things that could go to production. Similar comment regarding testing, deployment and operational use.]
The Executive Summary answer to the original question, in context... is --- "No."
But, I'm sure you have experience regarding other things that should be considered in the use of stops. And those would be of great interest to the CN audience! Tom