Do Adventurers equip items they buy as part of an advance order?

I know that if an adventurer is in your shop and s/he wants to buy an equippable item, a notice will appear (about the stat change that will occur if you sell the item in question to them) and the adventurer will start using the new item.

However, advance orders are a little different because the customers buy in bulk. If an adventurer asks for "2 pieces of armor" in advance, and I sell him/her 2 equippable items, will s/he equip them the same as if s/he had bought them singly?

Yes, however the adventurer will only equip the first item in the advance order, even if all pieces of armor are otherwise equippable.

Here we see Recette selling two pieces of armor to Charme as part of her advanced order. Note the box in the top-right corner, as it shows which of the items your adventurer will equip (assuming purchase).

As you can see, Charme is now wearing the Chainmail Shirt, but has kept her Wooden Bracelet. So make sure that if an adventurer gives an advanced order, you are extra careful the order in which you sell them items.