What will happen when I deploy a continuously running Azure WebJob with a QueueTrigger (queue connection defined in app.config) into a Deployment Slot (for example \"Staging
Yes, it will start running in the staging slot.
If you don't want this, then pointing it to a staging queue is indeed the way to go.
Update (11/24/2014): you can now chose to make certain setting & connection strings 'sticky to the slot' using PowerShell. See this post for details.