Never built one but the .204 is on a .222 Mag case which has the same case head size as the .222 Rem and .223 Rem. It should feed fine unless the .223 magazine has ribs to keep the cases to the rear in which case they'll be too far back. If not it should work fine.
I had a new Krieger in 204 put on my old Remington 700. It feeds fine from the magazine (it was a .17 Rem) and is the most accurate and easiest rifle to shoot that I have ever owned.
