What I did was 20x virgin cases (baseline) vs. 20x cases on 3rd firing vs. 1x case reloaded 20 times with AMP anneal between each firing.
Basically the only difference I saw was that the 1st firing (virgin brass) was 10-15fps slower on average in all situations. The AMP annealing kept the neck soft enough to never split and I eventually case-head separated the case at 22 firings. ES/SD was pretty much the same across the board, just a shift in the average after the 1st firing that stayed steady. No notable dispersion difference.
I haven't large-sample tested when cases will neck split, nor the effects of going 4+ firings without annealing, but I can say anecdotally around 5-7 is when you start seeing it and you can feel the difference when seating bullets. What net effect that has I don't know.
ETA: In general, my opinion on brass prep at this point is that you can go out of your way to screw things up by ruining brass, mixing mfgs, mixing lots maybe... But generally speaking brass prep is a waste of time. Most case weight variation is accounted for by variations in extractor groove cuts. ES in case volume is eclipsed almost immediately by orders of magnitude once the bullet moves into the bore. I size it, trim it, anneal it (purely for life span), and chamfer the mouth myself.
I did a batch of cases that I neck turned, neck honed, sorted by volume, deburred flash holes, uniformed primer pockets, chamfered and deburred. Next to a batch of randomly grabbed virgin cases that I chamfered/deburred and ran with, there was no compelling evidence to ever do the work in the former again.