You can prove this to yourself rather easily. Just ssh to a remote node and execute any command that lingers for awhile - say something simple like "sleep". Then kill the ssh and do a "ps" on the remote node. I guarantee that the command will have died.
Hmmmm ... vayu1:~ > ssh v37 sleep 600 & [1] 30145 vayu1:~ > kill -9 30145 [1] + Suspended (tty input) ssh v37 sleep 600 vayu1:~ > [1] Killed ssh v37 sleep 600 vayu1:~ > ssh v37 ps aux | grep dbs900 | grep sleep dbs900 18774 0.0 0.0 9360 1348 ? Ss 07:12 0:00 /bin/tcsh -c sleep 600 dbs900 18806 0.0 0.0 3800 480 ? S 07:12 0:00 sleep 600