Yes! It can be done. You should connect to AppWarp with FB id as username.
Then you can get the list of friends using FB SDK and get list of all online users using getAlLUsers() method of WarpClient.
Then you can compare all users with friends list. Whoever is online you can invite him with sendPrivateChat method by sending him the rooom Id.
When you invite you can create a room and set some property to represent that you have invited a player to that room.
If someone is not available online then you can send push notification to that user through App42.
When the invited player arrives he can see which room has the property being set to represent that he was invited.