BobDDuck
Island Bus Driver
Yep. Last year a guy was fired from both FedEx and UAL for trying a similar stunt. It bears repeating here, as this practice has unfortunately been recommended by a couple of legacy pilots in this thread.
New hires: Do not under any circumstance start class at your new airline while still employed at your old airline. You will be fired and have your nice new life ruined.
I asked (in an email) the new place if they minded that I would still be on vacation at the old place for a week when I started up, mostly so I could jumpseat across the country to get to the new job. They said no problem. I fedexed my ID back after I got done with my first day of indoc.