At the very least, any electrolytics should be replaced.
Even unused, they age and will no longer meet tolerance. Not to mention, that electrolytic caps just don't sound good.
But, as one who has upgraded more vintage, and not so vintage speakers over a couple of decades, I can state with near certainty, that caps do make a difference in sound quality.
A friend and I used to have a part time, cottage business upgrading and fixing vintage speakers here in the L.A. area, and upgrading caps always made an improvement.
This Ebay seller has a pretty decent recap kit available. Better than what came stock for sure.
Recap Kit for Klipsch KG4 Speaker Crossovers
But you could do better with even better caps, buying them on your own from
Madisound