Ideally that would be handled on the FS layer and completely transparent to all apps. Things would get synchronized once connection is restored.
Or more precisely, you can, but by choosing the most fresh file and people have lost work that way. There's a few "dropbox ate my files" stories out there.
And yes, default into choosing some one, with an extended interface for displaying and managing conflicts.
Perhaps the idea of plain text/binary files is a little outdated too.
*) Unless you believe this can be resolved by software - I'm afraid we're very far from that point yet.
Instead we got OneDrive, Dropbox and iCloud. Ugh.