Yes.

Insert
Exec=sudo /usr/bin/killall pulseaudio
into the desktop file.

But to get that working you will need a sudoers entry. Add a file into /etc/sudsers.d (example in this directory) and run update-sudoers.
Or, if you do not know how to do, just install sudsers. But this is security mess as it will allow user to execute every binary to be executed with root rights!