It really depends on the style of shoe. Something like a standard running shoe is going to have to be replaced fairly soon no matter how much money you spend on it. The uppers might hold together, but the foam itself is a consumable item. It can only bounce back for so long before it won't anymore. It doesn't really look obvious, but you might start to feel weird soreness or something that lets you know it's time to replace them.
"Barefoot" running shoes with no foam, or traditional boots/shoes with leather midsoles don't have that problem, so spending more can actually let them last longer.
Skate shoes, from what I know, are basically just standard sneakers for the most part, so they will have the same problem with the foam. If you are actually using them to skate, though, you might be wearing through the sole, or the upper, and in that case, a higher quality shoe might last longer.
TL;DR, it depends how you wear through them.