Hi Enclara,
There is a way to receive realtime notifications when you recieve an email but this will require an extra server, which is required. To be able to recieve real time notifications, on iOS, you would need to utilize the Symantec Email Proxy which handles requests between your CAS/EAS server(s) and the device(s). An impersonation account is required for the proxy to integrate, via API, to the Exchange Web Services server. When a new email is received, the Email Proxy will send an Apple Push Notification (APN) to the device with the email notification. This will also require Touchdown's latest version of Secure Email known as Work Mail. If you are looking to integrate this for your entire department, I suggest contacting Symantec Sales to work out the details.
More information on SYMC Email Proxy is available here. If you do choose to go that route, support would be there to assist with the setup.
-Adam