The "Local" subset of Construct 2 WebStorage maps to HTML 5 localStorage which, in turn, maps to applicationData.localFolder in Windows 8, and that is maintained on a per-application basis. You can store up to 10MB per app via HTML5 localStorage (and thereby Construct 2 WebStorage's set local value action.
It's not affected by what you do in Internet Explorer, and it will persist even when you update your application.
Construct 2 also exposes sessionStorage, but as you'd expect for a Windows 8 application that storage persists only for the current execution of the app, much as it persists only for the current browser session in a traditional web scenario.