Dropshipping or better know on eBay as 'Product Sourcing' is allowed on eBay.com - Link hidden: Login to view although the policy may differ on various eBay sites.
Ideally dropshipping works like this: You find a dropshipper and set up an account. Once you've created an account, all you need to do is grab the dropshipper's provided photos and product descriptions for the items you wish to sell and list them on eBay or your website.
After you make a sale and receive payment, you log into your dropshipper account, select the product you have just sold and take it through the checkout and pay for it. Enter the buyer's shipping details, and the dropshipper will package it up and post it.
But in case the money is not released as you mentioned, then you will have to pay for the item with your own money, many sellers use their own money to pay for dropshipped items.