I believe that would go against the Microsoft license for using the ribbon interface.
Check it out here: http://msdn.microsoft.com/en-us/office/aa973809.aspx
I don't have any use for it either, so I just put the "Exit" option in there.
EDIT: Here's the answer from the Office UI group at Microsoft - looks like the Application Menu is NOT optional:
Thank you for submitting your question. The design guidelines do stipulate that the Application Menu is required and it is a critical element of the Ribbon UI implementation. Different control sets may allow for the hiding or disabling of the UI element, but the expectation is that your finished application will still contain an Application Menu element (you may seek to implement it yourself as part of your window frame, or through other means).