Re: 338 Edge brass from 404 Jeffery's
No on the Norma. Norma brass is soft and the primer pockets won't take any pressure. Probably no on the Hornady brass too, but I have no direct experience with it.
I use the RWS brass because it's tougher than nails in the case head. But RWS ceased manufacture of it more than 10 years ago so it is tough to find now.