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No, that's not necessary. All you have to do is move the files from the html/ folder (including all subfolders and files, ie. the whole site) to the root folder, and adjust the settings in mainfile.php.
As a safety precaution, copy the files in your first attempt, not move them, and then change your mainfile.php settings to reflect the new paths. Make sure you set the CHMOD rights to the cache/ uploads/ and templates_c/ folders correctly (777 or 755, depending on your server setup).
After you've done that, login as admin and 'update' the system module. This will tell the system to use the new path.
Once you got that working, you can remove the html/ folder with all the old (and now unused) files.
For maximum compatibility, leave the html/ folder empty, create an index.html file that redirects to the root path, so anyone linking to the html/ folder will be redirected to your new site address.
Herko