I am afraid that functionality is not in BIM 360 or Revit to date, but it is a good idea. I was going to suggest putting it in BIM 360 idea's forum but someone has put it forward back in 2017. Autodesk has accepted it and added it to their roadmap. (see link below) Saying that why not put it forward again it is a great idea to speed the process.
Document Management: Ability to publish sheets to Docs directly from Revit
Now I have not used C4R for a few years now and cannot remember how it worked in there.
The only other way for you to get BIM 360 to export sheets out from your Revit model is to upload your models directly to the Plans area were it will export the sheets out.
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Gareth Spencer
BIM Technical Consultant | Man and Machine (UK)