You can of course set up these basses with lower action (unless they have some VERY serious issues), but you can't be sure that they can actually handle a lower action without introducing fretbuzz or "choked" notes. This will depend on the quality of the neck and the fretwork. It is impossible to predict 100% whether these basses (or any other basses for that matter) can handle a lower action without actually lowering the action and testing it. Of course, a trained eye can spot serious issues like a crooked/twisted neck or any severe problems with the fretwork, but even if everything looks fine you won't know for certain until the action is lowered and you actually play it. Maybe it will be great, or maybe the frets will need to be leveled. And some basses can't handle a low action even after the frets have been leveled to perfection.
Lower priced basses like these will generally need the action to be slightly higher than on top quality basses. And yes, the quality of the wood can make a huge difference. A neck made from poor quality, soft wood won't make a great instrument, no matter how perfect the fretwork is.
Ask the store if they can set up the basses properly for you. If they refuse you might as well buy a bass from one of the large online box shifters. They probably have a much better selection, and maybe lower prices too. Don't get me wrong, I think it's great that people support their local guitar stores, but if these stores won't provide a better service than the online box-shifters they really need to up their game or go the way of the dinosaurs. Poor service = they don't deserve your money. And refusing to set up an instrument in playable condition for a potential customer is VERY poor service indeed.