Well, the 7x57 it was designed for runs around 45,000 psi; the .308 Winchester can go as high as 62,000 psi. Your decision. No, it probably won't "blow up", but it won't last long on a steady diet of .308 factory loads.
Also, there is a question about how some of those rifles were converted. Some were re-barrelled, but others were rebored and re-rifled, then the chamber drilled out and a chamber sleeve installed. I have posted a picture of such a conversion at
http://www.thefiringline.com/forums/...5&d=1232476324.
Jim