After you create an email forwarder, if you don't want the mail to be saved on the server, the best thing to do would be to remove the account(s) completely and simply leave the forwarders in place. That way, mail would automatically be forwarded on to your gmsil account, etc., without ever being stored on the server. The server would act as a "middle man" in effect. You can accomplish this in cPanel by clicking "Email Forwarders," where you'll see the forwarders in place.
Email Forwarders operate independently of the Email Accounts, so deleting the accounts wouldn't stop the mail from forwarding, it would just stop it from storing a copy on the server itself. The emails will all forward, as the forwarders would still exist on the server.