You may receive a notification in an Android app when the SQL Server database occurs some change? In the Web application I used for notifications "SignalR" .
The newest Version is called "Firebase" (but GCM is still ok). I use it in my php scripts to send a message to the app (like WhatsApp, etc.
Workflow:
1. Register the device to GCM
2. Store the GCM-RID with the device/app/user-id to an own database (otherwise you will only have an abstract ID)
3. Call a Google server with data (see the example)
3. app reacts via intent
4. do your stuff