Yes, but there may be problems. Is the new barrel to be a GI replacement barrel or a new sporter barrel? If the former, things are fairly simple. Just use the existing draw line and fixed base to line things up, then (if a new barrel) run in the finishing reamer until the GO headspace gauge fits.
If the "new" barrel is an old military barrel, you may have a problem and have to get good headspace by trying a variety of bolts. With luck, things will work out without too much trouble.
With a new sporter barrel, things are tougher. You have to run the barrel in, bring it up to just about the right torque, then mark it, remove it and cut the extractor slot. Then reinstall it, bring it up tight, and finish ream the chamber to get the headspace right. This is assuming you don't want to reinstall the military sights; if you do, you will have to machine the barrel to size at the right places to do that, plus doing the drilling and slotting that are necessary.
The Mauser 98 is a lot simpler because the receiver has an inner collar that takes care of the extractor cut and allows the barrel to be flat at the back. Then it is only a matter of keeping the collar contact and the shoulder contact even. Plus, the sights on the Mauser were put on after the barrel was installed, where the sights on the M1903 were installed and the extractor cut made before the barrel was screwed into the receiver.
Jim