[Toadling]

I don't have any concrete information just yet, but from what I've read I don't think this will be possible.

When an app is in the background, it goes into a "quiescent state", meaning its state is preserved and the app is ready for action should you need it again, but the app can't continue doing arbitrary processing, like syncing OmniFocus data.

There are some APIs provided by the OS that allow certain types of processing to continue, like background audio or VOIP. But I don't see anything that would allow OmniFocus syncing.

-Dennis

PS - Here's a good overview from Macworld.