No. The Sonos app is not used at all on the Move when in Bluetooth mode. It is then just a dumb Bluetooth speaker. 

Seriously? That’s stupid. It wouldn’t be hard for them to make the app accessible from cellular data 

The Sonos app isn't even a music player. It is a remote control for the networked system. When connected to wifi the app is NOT getting the music over wifi and playing it. So it isn't stupid, you just have a poor understanding of the way Sonos works.

I do understand… the app is just a ‘middle man’ and all content on the app can be found through the official streaming services that provide them.  But I have added many stations/songs/etc to the actual Sonos app to not have to utilize multiple streaming sources for what I want. (Ex . IHeartRadio for my radio, Apple for certain playlists I created years ago, amazon for newer stuff, pandora for (IMO) the best genre/artist specific and closely knit random playing. 
So the app to me is a ‘one stop shop’ where I have all my sources in one place. 

Sonos radio was just released.  It’s possible that a separate app gets created later to play away from home.  It’s also possible that the licensing agreements they have don’t allow playback on anything other than sonos devices. 

I agree that it would be great to listen to Sonos radio outside of the Sonos app and speakers.  I don’t know why that hasn’t happen and therefore can’t conclude that the reasons why are stupid.