As an about to be new owner of a Prussian M15 Shako I am curious as to why they only have the national cockade on them and no state cockade on the other side? Is it because they often have those field badges attached on top?
I have never seen any photographic evidence showing both a Feldzeichen and a state Kokarde being worn at the same time. I have seen photographs of a Telegraph soldier and, I think, a Jaeger wearing a state Kokarde without a Feldzeichen. It's hard to argue with a photograph from the period, so I would say that it could be done. I am sure others have more insight into the rules governing Tschakos.
As an ex military officer I can just see the German Hauptfeldwebel chewing out some soldier for having both the Fedlzeichen and the state kokarde on his shako. Probably so he would look good for his girlfriend.....