Do you mean is it possible for you, or is it possible for Line 6? 

No, as it stands right now, it is not possible to get these sounds on a James Tyler Variax (though I imagine a 12 string model with the tuning set really high would come close to a mandolin).  There is no way to get any sounds onto the guitar besides what is already there except when Line 6 offers a firmware upgrade - unless you count fiddling with pickups and whatnot via Variax workbench. 

For Line 6?  I dunno, drop them a line and let them know you're interested in that having those sounds in a future firmware. 

http://line6.com/company/contact/productfeedback/