I'm currently running the latest stable release of CM7 for the HTC Droid Incredible and Facebook for Android 1.6.4 (released on 20 August). According to Facebook, push notifications are enabled for devices that support them. Since I get push notifications from other applications (such as Google+), I know my device supports them.
I've read about various problems with them, but I haven't found any definitive solutions (or a definitive lack of a solution). I would assume the setting for push notifications would be in the application's Settings menu. I have a number of options for various times to pull notifications down, but I don't see an option for push notifications in the app or on the Facebook website.
Is this just a broken application or am I missing something?