Kat,
For now, in a site with no internet access, assuming Moodle is already up and running, then for badges there are two considerations:
1) You should be able to make and issue badges without any problem even if Moodle is not connected to the net.
But students will be able to download badges they have been awarded and possibly then use them elsewhere on the internet. In a sense badges are just image files with special data in them. So, like any file, they can be emailed or facebooked, etc.
There is currently not a way in Moodle to prevent such downloading.
2) Each badge is given a unique 40 digit identifying number inside of it. If the badge is downloaded and saved by the student to their Open Badges backpack and the badge made public, then this number can be used in a URL that can be clicked on to take someone to the information page on your site about that badge.
Here's one of mine: http://2013.imoot.org/badges/badge.php?hash=68f147136711f857deccbd5e74d689a72b1da8a9
If your site is not on the internet, of course, they won't be able to actually reach your site. But the URL is there to be seen. And if your site ever does show up on the web, then those links would work.
One setting I suggest for badges is to turn off 'Site administration > Badges > Badge settings > Enable connection to external backpacks', since without an internet connection it won't work at all.