Do adventurers buy any equipment on their own in Dungeon Village?

Adventurers will buy their own equipment, but it's pretty random. Once you start getting buildings with decent appeal and quality, they will, for the most part, ignore the Weapon/Armor/Accessory shops, as you can't upgrade those. Giving them as presents is usually the more reliable way to upgrade them. Plus, it build town popularity, and adventurer satisfaction and work. And I have yet to see them use salves on their own.

Fun fact: on the off chance an adventurer DOES use the shops after giving them decent equipment, what they buy is mostly random. They can and will DOWNGRADE their equipment. So once you get in the clear for cash, you're better off replacing those buildings with stat increasing buildings instead.