As far as I can tell there is no way to combine DevonThink and Shoeboxed.com. DevonThink is a great tool for me to scan and label receipts, but Shoeboxed is a better way for me to store receipts and have expense reports prepared. Devonthink is a great way to search and study receipts where Shoeboxed seems clumsy. It would be great to combine these tools. But once the receipt makes it to shoeboxed I lose my cool DevonThink super powers.
Sorry but no - and as there doesn’t appear to be any official API, there doesn’t appear to be much you can do with it outside of their control.
(Speaking personally (as I am indeed “a person” 
), online services like this all make me nervous for people and their data 
)