Depends on the quality of the machining and finish of the new barrel.
Breaking in a high-end match grade barrel should not be necessary.
If you want a "rule of thumb", here's what I recommend:
Using a good quality rod, and a properly sized pierce-type jag, push a tight-fitting patch down the clean bore from the chamber end. Pay attention to the way the patch feels going through the bore. You're looking for a smooth, uniform feel with no tight or loose spots. For a froperly set-up and fitted barrel, the last couple of inches of the bore will be just a tiny bit tighter.
Any roughness you feel may indicate a need for "break-in". I use the Sinclair method for bores I sense need break-in. I have used Mac1100's method on a handi 25-06 that benefitted from the polishing treatment, even though it had been shot quite a bit when I got it.
There is no one method or rule for every barrel. I would try the "patch test" and then follow the manufacturer's recommendation. If the bore is rough, and the manufacturer advises against any break in, then I guess the tube would have to go back to the maker.