Hi there,
GDE does integrate with the visual editor by adding a button (TinyMCE plugin), but if the plugin is uninstalled it's completely removed - GDE does not alter any core files in any way. It also does not integrate at all with permalinks or the media library (in WordPress 3.5, anyway). Most likely you're having a different problem, but do make sure you clear your cache, etc. just to make sure it's not a fluke before you drive yourself nuts trying to sort it out. :)
Hope this helps.
Kevin