(This answer may be outdated after 2013)
Sorry to say, but you'll need to find some hardware to test this functionality.
Push notifications are not available in the simulator. They require a provisioning profile from iTunes Connect, and thus are required to be installed on a device. That also means you'll probably have to be accepted into the apple iPhone developer program and pay your $99.
On the bright side, with the iPhone OS 3.0 update, you can test this functionality on any device, including the first gen iPhones.
i ran into the same problem, you answer is not clear talking about second part of the question:
If isn't, how could I test that? Is there a free sample application compiled to do that? I created the Server provider, but I need test the functionallity.This is tutorial link for support Push notification in Simulator. medium.com/swlh/…
But I have some good news for you. Xcode 11.4 beta is out and the best part about this release for me is that we can finally test push notifications in the iOS Simulator! Following is the sample implementation - medium.com/better-programming/…