From my experience, dents may be in the dustcap in the middle of the bass driver in which case, unless the damage is extensive, it is likely no effect on the sound.
My first task in my first hifi job at a Tech Hifi that specialized in refurb gear, was testing used speakers prior to attempting sale. Those with voice coil issues, usually due to being driven by amp that was clipping, had to have drivers replaced prior to sale.
In many cases, the issue was merely a pushed in paper dustcap. Ugly and a defect for sure but no impact to sound. Solution: replace the dustcap, or the easy fix: use a safet pin to punch a small hole in teh dustcap and push it back out to normal from behind.
THese speakers were then sold at a discount determined by magnitude of defects, if any. Common practice to this day.
Dented soft dome or other material tweeters: different story. Any physical defect there is likely to have an effect on the high frequency sound. Could range from minor/not a significant issue to major. Devil will be in teh details.
From experience I learned never buy expensive speakers with exposed soft dome tweeters unless there is a grill or some other way to insure no accidents. If you have young children in the house: doubly true.