Well, no reason why they shouldn't work.
Funny. I've had several '06s through the years. I've stayed with Wby since 1970. Since 1950, I've loaded 52.5 grains of 4064 with 150-grain Hornadys, Sierras and Remington Bronze Points. I've used Remington 9-1/2 primers, regular Win. Large Rifle, Win. Large Rifle and Magnum. I've used Remington and Winchester brass. I've even mixed in US Army brass.
They all shoot to pretty much the same place; they all shoot about the same sized groups. I've tweaked the Wby around to 1/2"-5/8".
Maybe I should just stick with "I'll take luck over skill, any day."
So, I guess these new Winchester "pretty primers" will work just as well...
, Art