The closest you could get to this 'out of the box' would be to set up the promo with a list of email addresses it's allowed to be used by (under Promo Requirements) and then make the promo auto-applied. Once the customer is logged in with something in the cart, the promo will be added. Obviously that's not going to work if you intend the promo to be available to any customer, but that's the closest you'll get without customization.
With customization, like mmcgeachy said - anything is possible. The problem you're going to run in to there is that promos have to be paired with a CustomerID. A customer coming to your site from a link who wasn't already logged in before won't have a Customer record, so you would have to also change when Customer records are initially created, before you could add the promo-related customization.
Totally doable, but it's going to take some fairly involved modifications.