Azure WebJobs and Deployment Slots
Using slot sticky settings, you can now set
WEBJOBS_STOPPED = 1on the staging slot. This will prevent webjobs from starting on the staging slot, and the setting will remain on the staging slot when the code is swapped into production.
https://github.com/projectkudu/kudu/wiki/Web-jobs#configuration-settings
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.