Well this is kind of a loaded question , yes it can be done but I would reccommend fitting the barrel to the action like the Rem barrels do thus eliminating the barrel nut.
Savage did make some RUM's mags and WSM's with the standard small shank but quickly changed to the larger shank that they are found in today.
I have heard of cases that the small shank guns chambered in the RUM's had split the barrel nuts in some higher pressure rounds and supposidly this is why Savage went to the bigger shank and kept the barrel nut instraed to just fitting them up like everybody else.
Now a question on your cartridge choice , why do you want a 338 RUM improved?
The reason I ask is that the RUM case desgine is already very effecient and little gain will be had by improving the 338 RUM. You will have to fireform you brass to get all the benifit out of it and that eats up barrel life and is time consuming and all for very limited increase in power.
You could go with the 338 Edge which is a 300 RUM case thats necked up to 338 , the 300 RUM case has more powder capacity than the 338 RUM case thus giving you a boost in velocity with the increased powder and their is no fireforming.