I think you can already use the Mobile SUICA app to ride Shinkansen, as these YouTube video demonstrate:

NEX requires the extra fare class (特急券 / グリーン券) just like Shinkansen, and the app clearly shows the ability to purchase them from the videos, so in theory it should be possible, but I guess unless someone tries we won't know for sure.

I wonder if they will eventually allow people using JR Pass to convert paper tickets to mobile ones or have a mobile JR Pass, as that would be great!