You should be able to work with push notifications. It depends on what type of push notification you are talking about, such as SMS, App notification, Setting, etc.
I would initially record the test with Mobile and see what type of object is captured. If there is no object captured, you have the ability to work with more advanced tools, such as the Mobile Object Model. You can find different methods, such as IncomingSMS method, IncomingCall method, Exist, etc. that you could use to work with the type of notification you have.