Reinstalled my MacBook Pro, resync with iPad issues
I do this all the time - introduce an iOS device with content to a new library (whether it's on the same or a different computer).

In your case, if you simply don't sync until you reintroduce the last good backup of iTunes then everything will be fine again. But let's assume you don't want to do that and continue with the question as asked.

You can cancel the sync when the warning about erasing the content appears. At that point go and deselect the automatic sync option so you have time to transfer the documents.  

Then you can use the File menu 
Transfer purchases from "device" to get all the "apple iTunes store" content into the new library. This is a smart merge so you don't get any duplicates. Lastly, inspect the Apps tab to check for any third party data you might want to transfer. 

I also use the iBooks email to get a few PDF off an iOS device but you may want to look into trying and later purchasing PhoneView which lets you move documents to/from your device to a mac with ease. It's very powerful and goes far beyond what iTunes allows.