Not necessarily an Internet connection, but definitely a local network. Before we caved in and started using Quickbooks across the board for both invoicing and POS retail in our storefront, the bosses had me whip together a custom POS based on parts of OpenBravo and OpenPOS. I was running a virtualized, modified OpenBravo ERP server that was connected to the front register running a heavily modified OpenPOS front end. It was quirky, buggy, and ugly, but even if we lost Internet we could still operate as long as the LAN stayed up.
Now we're using Quickbooks for everything, because our accounting office wanted easier reporting. It's a nightmare, but at least we have good outside support across the board, instead of me being on call 24/7.
I'd love to give your project a shot in my spare time, and see if it might be useful for inventory management if nothing else. Quickbooks sucks in that area without their expensive add-ons.