I'm not sure how to make Outlook automatically execute this, but there is a way to have a macro automatically close Outlook:
In MS Outlook go to Tools->Macro->Visual Basic Editor
Copy/Paste the following into a Module then save and exit from Visual Basic.
Sub ExitOutlook()
Application.Quit
End Sub
If there is no module, right click on the project and select 'Insert->Module'
Back in Outlook, go to 'Tools->macro->macros' play 'ExitOutlook' and it will shut down the program.
Another option is to ask this question in some type of VB forum and get a better answer so you could run a batch file that first runs a VB script that locates and closes any Outlook windows and then performs your backup.
Hope this helps.