That is, I really like the feel and responsiveness of these gadgets (much better than LyX, for instance) and would like to use them offline. Is this actually possible? Are there licensing issues?
Sure, the editor and preview components are open source. It's released under the MIT license which is one of the most permissive copyleft licenses in existence.
You'd need to make your own customized bits, but it wouldn't be entirely difficult to have it work entirely from local storage. If you come up with anything neat, feel free to share it :)