Yes and No, a lot of care needs to be taken to make sure the reamer feeds straight into the old chamber.
It's not difficult but it's not as easy as cutting a new chamber from a bore.
I refused to recut a chamber in a 30-06 one time for a fellow who wanted it to become a 300 Win mag.
Remember, with the larger diameter body, there isn't a pilot guiding the reamer true to the axis of the bore. Not only that but the reamer is making the initial cuts with its shoulder, which can quickly lead to chatter and that can be hard to clean up to impossible to clean up.
The 30-06 reamer starts to bite into the side wall of the 8x57 chamber appx 3/4 of the way down, and the tapers are close enough that it still works well with a floating reamer guide, but you still need to be extremely careful, especially if you're doing the job with a 30-06 reamer and chasing the neck/throat with a separate reamer.
First, you have to swap out the bore guide on the reamer from .308 to .323 if it's rotating or shrink fit a sleeve onto a solid guide and turn it to .323 so it will work as a guide while cutting the chamber. If it isn't fed true or for some reason wanders, the barrel is ruined.