If you referenced a local copy of the firebase.js lib, it would work as well as the remote copy, at least initially. Since Firebase is in beta, changes can be pushed to that lib at any time, making your local copy obsolete.
Utilizing a local copy wouldn't, by itself, solve the issue you are hoping to address. While Firebase will survive temporary outages and spotty coverage, there is no locally stored copy of the data, so you'll need to either connect to Firebase initially and obtain that data, or use set() to create some sort of local default if offline.
More robust offline support is on the Firebase road map.
Some additional and very informative reading can be found here: