Yes. The AA gun would still belong to Germany (put a German control marker under it to denote that fact), so Germany’s Radar would still apply. This would be true even if there’s an Italian AA gun there. The rules simply say that only one AA gun may fire at a time. They don’t say which one it has to be, so it’s up to the owning player(s).
If Italy were to be captured by the Allies, the AA gun would then belong to the capturing power, so Radar would no longer apply to it (unless that power also has it). If it were to then be liberated by the Axis, the AA gun would belong to Italy, and have no Radar enhancement (again, assuming Italy doesn’t have it also).