Tarball Extraction

Is it possible to extract a tarball with the file manager?

Not right now...

Best chance for user is to just upload all files within the tarball, if you have ssh access, you could upload the .tar.gz and ssh in, extract with following command:
tar xzpf <tarbal>
Note that most tarballs do have a directory in them, so watch out you don't get something like:
/home/<user>/<tarball>/<extracted tarball dir>/

Hope this can help you