RE: Would it be OK to........
Or you could do this. Whatever you do, try to keep the length of the wire/antenna the same length. The P3 antenna will fold down automatically, and can be used as a functional antenna or cosmetic. Coiling the antenna lead around the plastic tube does not affect the range at all. Just keep the coils seperate. The photo is of the system installed just for fitting in my article about eletrical hygene. On the P3 innards photo, I just notched the rear extensions and put the wire there. He will be changed on my next P3 to make the prototypical antenna functional.