Have user register or login on cart instead of checkout in drupal commerce
Is it possible: Yes.
Should you do it: No.

Why?

Having the user account pane at the the cart is a bad idea, since it probably would be very complex to do, and that there isn't really anything that hinders the user to start the checkout flow. You are also forgetting a very important thing.

The Commerce checkout flow is very customizable. This means that you can define extra pages in the checkout flow, and via the interface customize what should be displayed in each page. A much better solution would be to create an initial checkout page with account info only, an extra page that displays info about the order being validated and not allowing to process the order until it is approved. Once approved, the link could simply be that checkout page which with the updated order status can be skipped.

This will keep the customer in the checkout process and leverage the Commerce flexibility.