This is exactly how Amazon got its start: Jeff Bezos didn’t have a stockpile of books; he only ordered them when a customer made an order on his site. The difference of course was that he did physically handle the books.
If that's how it worked, then it wasn't really drop shipping. It's not drop shipping because the goods didn't go directly from vendor to customer. That's more like Just in Time fulfillment.
https://retailops.zendesk.com/hc/en-us/articles/202763175-Se....