That's pretty close, but it will be a bit more work than that. The shoulder on the 300 PRC is pushed back slightly farther than the 375 Ruger case. You can do this with the 338 RCM die once you get a feel for it, but you'll probably crush a few cases in the process. Ideally you'll want a 300 PRC case on hand to setup the 338 RCM die.
Here's another option, but one that won't work with all actions. You can form 300 PRC cases from 8x68s brass without too much effort, but the rim diameter is a little smaller than a standard .535" magnum bolt face. Some actions will work with the smaller rim, some won't.
left to right: 8x68s RWS brass, 375 Ruger case, 338/375 Ruger formed from an 8x68s case, 300 Sherman Mag (300 PRC Improved) formed from 375 Ruger brass, 6.5/375 Ruger from 375 brass, 7mm LRM formed from 375 Ruger brass.
You can see the difference in the rim and case head between the 8x68s case and the 375 Ruger case. The 8x68s brass will result in reduced case capacity, but not enough to cause a major drop in performance. I think it would actually be easier to form 300 PRC brass from the 8x68 case than using 416 Ruger brass.