Is it possible that a too tight rear wheel quick release can cause shifting issues?
Yes, this can happen as a result of variance in how hard the QR is tightened causing variance in the alignment of a replaceable rear derailleur hanger. Typically this relates to lack of precision in the manufacture of the hanger and/or dropout and consequent poor fit of their interface. Sometimes by taking the hanger off and studying the interface you might observe spots of paint or material to remove that are clearly making the interface not lay flat. Other times one of the surfaces isn't flat.
Here's what I would typically do:

Make sure the QR skewer is working well and easy to get to a high clamping force. This can mean lubricating it if it's an external cam type in good condition, or, the best plan of all, replacing it with a good quality internal cam type such as Shimano.
Remove, clean, lubricate/loctite, and tighten whatever hardware holds the hanger on.
Get the wheel back on with the skewer as tight as you'd normally have it. Usually when bikes have this problem you can see the hanger flex around and chane alignment as you tighten the skewer.
Align the hanger to be aligned in that state. The reason you want a good skewer in this situation is that they easily get you to a high clamping force range, and the way it tends to go with bikes having this problem is that you won't see the variance once it's in that range, more only with skewers that are barely doing their job, as in many external cam ones and especially unlubricated or in poor condition.
If that doesn't work, replace with a CNC hanger such as Wheels Mfg, which will tend to help make the fit better. (It's not a sure thing because some or all of the issue can be in the dropout though.)

Fatigue from repeat alignments is its own concern but will not itself cause this problem. I can imagine a replaceable hanger getting bent in a way where the mating surfaces weren't flat anymore after aligment, and this problem resulted. I've also seen brand new bikes do this.