Can I ask what version of the System software you are running? The term “process” only recently became supported in osX. Up until 10.2.4 or .5 it was still listed as unimplemented according to the finder dictionary. I ran my version of the script on 10.2.6 it should also work in os 9.
You can try this in versions of osX older than 10.2.6
set psList to do shell script "ps -auxw | grep "Mail""
if psList contains "Mail.app" then tell application "Mail" to quit