I don't think it's possible but I would really like to see it added as a feature. I need access to a bunch of documents offline and syncing them through iTunes is a pain.
Currently, Acrobat Reader for iOS does not provide an option to download cloud documents to your iPad/iPhone.
The following forum thread describes a workaround.
If you have a large number of documents that you want to view offline, a more direct approach is to transfer documents from your computer to your iPad/iPhone. You do need to use iTunes and a USB cable. But you just need to use the File Sharing feature (without syncing). Downloading cloud files to your iPad/iPhone over Wi-Fi would take significantly longer.
Please take a look at the "How to transfer PDF documents from your computer to your iPad/iPhone" section of the following FAQ document.
Transferred documents on your iPad/iPhone will appear in "Local" (file location) in Acrobat Reader, and they will be suitable for offline viewing at any time.
Please let us know if you have additional questions.