Such as in this photo
And what benefits are there compared to wielding it facing up?
Absolutely. It is pictured in numerous medieval and modern fencing treatises (though double dagger is less common).
http://www.alliancemartialarts.com/Solthurner-7a.JPG
http://i.ytimg.com/vi/CD0EbGpemLk/hqdefault.jpg
http://www.thehaca.com/pdf/sf15.JPG
The grip offers generally stronger downward thrusts and hooking capability.
For great discussions see these videos below from HEMA instructor Matt Easton from Scholagladiatora: https://www.youtube.com/watch?v=bRB9h8D3xao https://www.youtube.com/watch?v=CD0EbGpemLk