I think its mostly geographically specific. IN MY AREA, permits or lack thereof, is not a serious issue. Actually, they're not much of an issue at all. I've appraised probably about 10K houses in this area in the past 30+ years and checked for permits less than 20-30 times, total.
I also know that nearly any older home, 30+ years, likely has modifications/updates for which permits were never pulled. Unpermitted items like decks, fences, yard barns, pole barns, screened porches, updated kitchens/baths, new HVAC/plumbing/electrical are so common that they aren't even a blip on anyone's radar.
I appraised a house on 25 acres a couple of years back where the owner had converted the SFR to a duplex and, he built another duplex on the property, all with no permits. I know one of the building inspectors pretty well and called him. Didn't reveal the address but told him the situation and asked what he'd do if he knew about it. His reply was basically that they probably make him get a permit and inspection and fine him a few hundred $$, at worst. BTW, the Assessor had the conversion and the additional duplex on the property record card. To say they're pretty causal about permits on existing homes is an understatement. New construction is a different story.
If your engagement letter says to check permits, you should check permits. Report the lack of permits in the appraisal and let the lender decide what course of action to take, especially if you know that the absence of permits has no effect on the value.
But, if you live in an area where you know the permit police are neo-Nazis, you should always check, even if your client and engagement letter is silent on the issue.