The Bridge doesn't need an Internet connection at all--it will come preloaded with some firmware version, and all hub discovery and setup can be done entirely over your LAN. That being said, you may want one for firmware upgrades (they haven't released one for the v1 Bridge since February of 2018 and will likely never do so again, but you might be able to get updates for bulbs/accessories, not that I think there have been any noticeable changes/fixes for their use with a v1 Bridge...and if you buy a used Bridge, who knows how long it may have been offline). After that, though, without their cloud features, I guess it would be as good without Internet as with it...and maybe a little better given that it will be running an outdated OS. 
Download the Hubitat app
