Hi Shwetha,
A workaround would be to install the 'notification_allow_temp_address' option. This option allows the Manual Notification to send to manually-entered SMTP e-mail addresses, rather than only to registered Contacts. So this will require human intervention rather than an automatic relay.
Alternatively, you could write yourself executable (.bat or .cmd) that calls the pdm_mail which you can call in Service Desk via the Remote Reference. This can be attached to the case via an auto event every time a new ticket is created.
Run pdm_mail -h on command line and you will see how my last suggestion could be used effectively ;-)
Kind Regards,
Brian