I'm not sure how flexible the phone gap plugin is regarding background processing, but yes, you may provide any payload you'd like when you create the message to push to your devices.
If you look Apigee's Creating and managing notifications document, you'll see in each example, there is a that can specified. If it is a JSON object (instead of a string), it will be delivered "as is" to the client. In other words, you could specify during notification creation that the for your notifier is something like:
{ "message" : "my message" }.
Hope that helps.