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A periodic error one would expect to be predominantly non stochastic (random). If ever circuit of the gears has varying motion you have much bigger concerns to settle. Yes if that were the case motion could be smooth or jerky - I don't know what you are assuming.
But if an error is significantly consistent it can be distilled (averaged) inverted and modeled out - think of how active sound dampening systems can kill 80% of regular noise (like a jack hammer) when switched on.
Seeing error can be modeled out with multiple runs and few simple f or z tests given you'd expect a Poisson distribution curve (a.k.a. a normal distribution curve). If tracking errors changed with temperature over the course of a night you'd have a greater challenge modeling this out unless you modeled PE against temperature and had a more sophisticated PE system that had a temperature look-up against multiple PE tables.
Large smooth error is simple to guide out. Consistent error can significantly trained out. Large, jerky, inconsistent tracking errors are a total pain - shifting weight balance alone may or may not help depending on why the gears and bearings are causing said behaviour. Put simpler I can see mechanical machining issue where weight imbalance would help and other situations where it could hurt - or of course the situation where both types are encountered in a revolution of the gears.
PE training is an averaged, non temperature adjusted 360 lookup table of your entire gear though one complete revolution of the worm (versus the main gear). It should help remove consistent errors and most users who share there findings online say it does.
My mount for instance knows exactly where it is when you start PEC training - be it on gear tooth 1 or 360 or anywhere in between. Average enough runs and you signal to noise in track error should be so high consistent error is mapped out - and that is all PE correction training should ever be.
Backlash plays multiple roles and it certainly comes into consideration when issuing corrective commands. If backlash settings are poorly modeled then executing any correction - from PE or auto-guiding - can make things worse.
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