Yes, you can set up the Reports Console to run tasks even when a users is not signed in.
If that's not working you'll want to double check the settings. One thing that you may want to verify is that when you're running Reports as admin you can see the intended settings. At times when you're running an application as admin it will be pulling information from a different profile and the settings wouldn't be the same.
If you want to dig into it further here's a couple of resources for finding out what's happening when scheduled reports aren't running:
LEM scheduled reports are not working - SolarWinds Worldwide, LLC. Help and Support