The extension would still need to recompute it once every time it is starts up, but since it is computable I don't think it belongs in LocalStorage. (You wouldn't store something like this in the registry if you were writing a Windows program; you'd just keep it in memory.)
Also, the article could use a bit of improvement in terminology. When it talks about 'loading the extension', it really means displaying the popup. I think of loading the extension as in starting up the background page via the extensions window.