Here is a quote from Fred Moreo of Sharp Shooter Supply. Not to discredit Kirby or Kevin, but I would trust Fred's opinion.
I get this question 15 times a week. The short answer is no, the Savage action was never engineered for cases that big. I have discussed this with several engineers and custom action builders, that all came to the same conclusion. A case of that size needs a .750" diameter bolt, and a 1-1/8" barrel shank, minimum.
I know from personal experience on a gun that I built for myself that after less than 100 rounds, it experienced lug set-back. There is not enough surface area on the bolt lugs for that kind of pressure, let alone enough to provide a cushion for over pressure.
There are several custom action makers that will build express actions for those class of cartridges. Probably the most reasonable is Stiller's Precision firearms. Sako made some in .338 Lapua, in a tactical rifle.
The .338 Lapua seems to intrigue alot of shooters that "must have one", but I would suggest before you jump in with both feet, find someone that has one and beg to shoot it first. You might change your mind about what fun is all about.