Necking down that far will be easy IF you use a good case lube - I prefer Imperial Die Wax or Unique, finger applied. Annealing before doing it may or may not be needed, try it both ways and see how it does. For sure, anneal it afterwards or it will split fairly quickly. As mentioned above, it will be really easy if your own or can borrow a 7-08 FL die as an intermediate step. But, I've taken .308 to .243 in one step with a high rate of success.
GI cases tend to run a little thicker than commercial but not massively. And it won't change massively when you size it down that far either, you'll add about 17% to the thickness, couple thou maybe? If it needs turning or not depends more on your new chamber than the cases, as such. When you get the new rifle fire a few factory loads in it, measure the fired neck diameter to see if your reformed cases/oaded ammo is larger or smaller. If your stuff is larger you will need to turn them down to about the diameter of the fired cases.