It is possible.
https://twitter.com/jaysix22/status/907617028722364419
https://twitter.com/SimGuruDuke/status/908156731141890049
And According to the official FAQ
How will the Gallery work and how can player share user generated content?
The Gallery will not be available in the Xbox One or PlayStation 4 versions, but players can still share their experience using the social features that are integrated into those platforms.
So they had a simple online exchange and uses the sharing program that the console use.
Speaking of the gallery, I have two Theories,
1.It maybe because they are focused on polishing the game and bug fixing, rather than adding a new feature.
2.Maybe because the files on pc are different on how they work on console.
But yeah the Gallery is possible and for the meantime, players can share content depending on the console.
Edited to add the question.