Is it possible to connect to a PowerPivot model in an Excel .xlsx file? (Not hosted on a SharePoint site... just the local file).
It must be, since Tableau can do it
You can build a VSTO addin.
Here's a site that helps explain working with PowerPivot and VSTO.
http://blogs.msdn.com/b/analysisservices/archive/2011/08/04/how-to-build-a-vsto-based-powerpivot-workbook.aspx