Welcome to the forum hhazen :)
As fudjj said it is possible. Oftentimes, it is ideal to keep 2-3 pieces (of the product you listed from a dropshipper) in stock just to be sure you have back-up whenever your dropshipper suddenly runs out of stock.
This is where live data feed comes very handy - since it gives you live updates of your suppliers stock levels.
May be you can list products from a dropshipper that offers this feature to avoid such an awkward situation.
All the best!