Can customers still order a product when it is out of stock?

Yes, for Simple products. In the product's Inventory section, turn on Sell when out of stock. Customers can then keep ordering after the quantity reaches zero.

The same section has the other stock settings:

• Track inventory on or off.
• The Quantity in stock.
• A Low stock alert level.

Variable products set stock on each variant and can't take orders once a variant is out of stock. If you would rather let shoppers wait, the In-Stock Notifier emails them when the product is back.