What'll more likely happen is that you'll get offered a job at a regional or ACMI first. A few months later, after getting some "real" currency, you'll likely have a shot at the majors.

Then again, like JM said, if you're looking to come back in a few years the majors might be pretty desperate for anyone that meets the new FAA guidelines they might just take you.

But I think the first scenario is more likely.