for the moment the answer is no...
Let me expand on that statement.
In many ways, your question is similar to this Q&A:
Ubuntu Tweak only offers (currently) a limited API call for the executable itself.
Therefore - when trying to invoke a Ubuntu-Tweak feature when starting from startup applications or via a quick list, you can only use the command line parameters that have been made available.
ubuntu-tweak -f janitor is one such feature. There are no command-line parameters (currently) for what you are seeking to do.
You can test this yourself by running ubuntu-tweak -h. The linked answer above shows the typical result you could expect.
Some programs - once running - expose an interface such as dbus that allows you to invoke features via an external program. Rhythmbox is one such software with its rhythmbox-client which can be called externally. Ubuntu-tweak unfortunately does not offer the same external interface.
What you'll need to do is submit a patch to the author that would add a command-line parameter to do the function you are seeking.
Alternatively - add an externally callable interface such as dbus when ubuntu-tweak is actually running.
I know you already got your answer, but I somewhat recently went through ubuntu-tweak's source (when it was announced that it wasn't going to be developed any longer) and translated everything that it did to the equivalent in bash. If you're interested to know, Ubuntu Tweak does nearly exactly:
sudo rm -rf /var/cache/apt/archives/*.deb
sudo apt-get clean
rm -rf ~/.cache/google-chrome/Default/*
rm -rf ~/.cache/chromium/Default/*
rm -rf ~/.cache/telepathy/Cache*
rm -rf ~/.googleearth/*
rm -rf ~/.cache/gwibber/
while read -r line; do if [[ "$line" == Path=* ]]; then rm -rf ~/.mozilla/firefox/${line:5}/Cache/*; rm -rf ~/.mozilla/firefox/${line:5}/OfflineCache/*; fi; done < ~/.mozilla/firefox/profiles.ini
while read -r line; do if [[ "$line" == Path=* ]]; then rm -rf ~/.thunderbird/${line:5}/Cache/*; rm -rf ~/.thunderbird/${line:5}/OfflineCache/*; fi; done < ~/.thunderbird/profiles.ini
rm -rf ~/.opera/cache/*
dpkg --list |grep "^rc" | cut -d " " -f 3 | xargs sudo dpkg --purge //this one may be dangerous. only run if you know what it's doing.
rm -rf ~/.cache/software-center/*
rm -rf ~/.thumbnails/*
dpkg -l 'linux-*' | sed '/^ii/!d;/'"$(uname -r | sed "s/\(.*\)-\([^0-9]\+\)/\1/")"'/d;s/^[^ ]* [^ ]* \([^ ]*\).*/\1/;/[0-9]/!d' | xargs sudo apt-get -y purge
And here's a link to my original comment on the matter from reddit.
Best Answer
As Donarsson pointed out in his comment, I think you just need to update. Ubuntu Tweak works fine for me in 13.04.
In a terminal, type these commands: