I work mainly on my Mac. Occasionally I’ll use DT on my iPad, and it always takes a while syncing just when I want to start working. Is there any way for DT to sync in the “down times”, when I’m not using it, so it’ll be synced and ready to go when I want it?
No this is not possible.
If you plug the iPad in, set it to never auto-lock, turn the brightness to zero and let it sit there with DEVONthink To Go open and it would be updating ‘in the background’. However, I don’t know what keeping it plugged in continuously for long periods of the time is going to do to the battery.
I only use this technique when I have done something that will cause a massive sync (over 30 minutes) between the iPad and the Mac (or iCloud). So far that has only been when I built out my 10GB set of databases on the Mac and wanted it on my iOS devices.