I am still hoping to get her natural tail longer/thicker before start of next show season otherwise, I can't imagine entering her without extensions. I know it shouldn't count against us, but... her tail currently falls right at her hock.
It takes a long time to grow hair. If it's currently at her hock, I would NOT expect you to have a show-ready tail by the spring.
Appearance does count and IS actually part of the scoring for showmanship. While you still need to have a good pattern, you will score better if your horse has a "full tail".
While it's not technically scored in the other events (horsemanship and trail), there is something to be said of first impressions and appearance. If there are two horses that performed about the same, the one that looks better will be the one that stands out to the judge. It's the honest truth.
Previous owner showed with extensions extensively... Does that cause any damage/stunted hair growth? In other words, am I fighting a losing battle and should just go on and invest in the extension?
No. Using a tail extension does not damage the tail. You only have the extension in the tail for the events, and then you take it out. And you do so carefully, so as not to damage any of the hairs. But you should be handling the tail carefully anyway, to always minimize breakage.
And some of it is just genetics. My grey will never have a thick tail. He just won't. He's a classic grey with a thin tail. <img style="max-width:100%;" src="https://www.horseforum.com/images/smilies/icon_cool.gif" border="0" alt="" title="Cool" class="inlineimg" /> My black horse (not pictured) has a gorgeous long thick tail to the ground. He doesn't even need an extension. And I do nothing different for him. But him, he actually has hairs growing on the backside of his tail dock. I've actually never seen that before. So that's why his tail is so amazing --- just lucky genetics. He's got extra hair!
So again, some of it just depends on the horse. Some are simply not blessed with good hair.