1) Your app isn't "interacting with the current instance of ArcGIS". Creating a new MxDocumentClass instance triggers the creation of a new ArcMap application instance, it doesn't cause it to link to an already running instance. Perhaps this is what you meant, just wanted to clarify.
2) In theory you'd expect that starting an instance of ArcMap should trigger ArcMap to check out the appropriate license; however, you may need to check out the appropriate license in your app before you can use the API. Worth trying.
3) If all you want to do is do automated plotting using one of the Export*Classes you may want to use the ArcEngine controls instead i.e. create a C# Form that hosts an ESRI.ArcGIS.Controls.AxPageLayoutControl. You can create the form hidden and then use the page layout control to generate the export files. Much lighter weight solution than starting and trying to automate ArcMap.