Represent bonds spanning a unit cell boundary plane
As the developer of both Open Babel and Avogadro I can say the answer is "not yet."

The main thing isn't the file format. It's that Avogadro at the moment doesn't have support at the moment to show bonds across a unit cell.

I believe there was a patch for that, but it was too slow for typical use:
https://github.com/dlonie/avogadro/commits/ENH_intercell_bonds