Programmatically find device support GPS or not?

Yes, this can be done.

You can call LocationManager.getAllProviders() and check whether LocationManager.GPS_PROVIDER is included in the list.

Just for reference, I believe all released Android phones come with a GPS. It's not something that Android seem to be worrying about, e.g. mentioning GPS as one of the device attributes returned by PackageManager.getSystemAvailableFeatures().

Those methods are easier to use:

private boolean hasGpsSensor(){
        PackageManager packMan = getPackageManager();
        return packMan.hasSystemFeature(PackageManager.FEATURE_LOCATION_GPS);
}

• true: available (activated or not)
• false: not available

So, in case of true, we can use

private boolean isGpsEnabled(){
        LocationManager manager = (LocationManager)getSystemService(Context.LOCATION_SERVICE);
        return manager.isProviderEnabled(LocationManager.GPS_PROVIDER);
}

• true: enabled
• false: disabled

With this two, you will know if GPS is available, activated or deactivated

There's also LocationManager.isProviderEnabled(String provider) method.