Uninstalling and then installing the Extension Manager should not affect the extensions installed in Dreamweaver, but its possible that they may not show up in Extension Manager after this. The reason this is, would be that Dreamweaver has a configuration folder that stores the files that the installed extensions need, which is different from where the Extension Manager stores which extensions have been installed.
Judging from the situation, it seems like uninstalling and then installing the extension manager would be the next step to take. I have never uninstalled my Extension Manager, so I cannot be sure whether the extensions will be removed or not.
