Everything is feasible. It all depends on the amount of work you are willing to put into it. You may look into the APIs of some 3rd parties (like UrbanAirship or Parse.com) that support push notifications to multiple platforms, to see how their APIs support these multiple platforms.
You should realize that APNS and GCM use different protocols (APNS has its own binary format over TCP, while GCM supports HTTP and XMPP), have different device identifiers (device tokens vs. registration IDs), have different payload parameters and payload max length, etc...
Due to those differences, at least in the end points, it wouldn't be the same server code that sends notifications to both APNS and GCM.
You can still have a lot of common code that is platform independent, such as the code that composes the notification to be sent, but the sending itself would be different for each platform.