Yes, that's absolutely possible and is commonly done.
OK thank you, do you happen to have a link to a tutorial on how to do this?
You will need to go to the Alerts tab > Notification Settings
From there you will need to setup a rule for your specific notificaiton.
Make sure you have your email plugin setup first though.
(Administration > Management > Outbound Settings)
There are no rules that I know of that will alert/trigger alert for an ICMP connection down..