Not without central software running 24/7 on a server to track this and a figure budget.
You can set up a policy server and encrypt your PDFs with policy encryption. You will need to deploy LiveCycle for that and this is an expensive solution which makes sense only if you need to encrypt this way a large number of PDFs.
Even with Adobe's LiveCycle Rights Management, there is not a way to automatically enforce that a user can only open a particular document one time at most. Instead, you set time periods for validity, but can manually revoke access to a protected document.