I did that a lot years ago, when Wby brass was expensive, and H&H brass, powder, primers, and pulled surplus bullets were relatively cheap.
It worked, but I did notice the case necks were a bit shorter than on the Weatherby brass.
I also have a 375 Wby in an FN action Sako, and I fire-form brass for it with the same results, slightly shorter case necks.
I fire-form 257 AI brass and 7X57 AI brass and have clocked the factory ammo shot in the AI chambers. For what it's worth I got about 200 FPS slower velocity than the factory claims in their tables.