Most likely Airwave is getting that information via SNMP Polling, where Airwave will initiate a "get" to the controller.
Not being able to receive alerts from the controller you will miss:
- Authentication Failures and radius server down
- IDS/IPS traps
- Access Points being down (SNMP polling will reveal this, but only during the polling interval)
- User Roaming Traps
That is just a subset of what you will miss.