I think this would be tricky. beorg uses a variant of Scheme rather than Emacs Lisp for the init.org. Also whilst there are some beorg variables which have the same names as the Emacs variables they may not always work in exactly the same way or support the same number of options. beorg doesn't contain any code from Emacs or Org mode - and I never look at Emacs/Org mode code when implementing features, just the behaviour. One reason for this is that Emacs/Org mode are GPL licensed whereas (at least currently) beorg isn't free software.
One potential idea is that you could write some Emacs Lisp to generate a beorg init.org based on certain variables set in your Emacs configuration.
If any one does do anything around this it would be interesting to hear the approaches taken.
Ah, I see.
I was mislead by "sync between devices". I guess this means between iOS devices only.