How do I answer that?
the handle without the right code goes into the void. Once you've entered the right code, you can press the handle and operate the door lock. So there's no need to lock the door, because you can only open it by pressing the handle with the right code.
However, I don't understand the question about the recessed lock, because this system replaces the handles, not the lock.
According to my research, it will fit if your Glutz mortise lock fulfils the usual Swiss standard dimensions.
The Yale Code Handle requires:
Swiss lock standard (CH standard)
8 mm square (standard in Switzerland)
Hole spacing 72 mm (handle height)
Door thickness 35-80 mm.
According to your description, this door handle should be correct.
The door is opened by entering the code, which is why a key cylinder is not required here.