The main reason you break in a new barrel is to make it easier to clean. If there is any improvement in accuracy, it's nearly impossible to measure. That said, if you are talking about hunting rifles that get cleaned a couple of times a year, it's not worth it to break them in.

On the other hand, if you have varmint rifles that might get cleaned ten times in an afternoon's shooting, it is worth doing. You can break in any barrel at any time as you are just smoothing out any tiny rough spots remaining in the barrel by shooting thru the totally clean barrel. The point of complete cleaning before the next shot is to expose the ultra tiny burrs to the next bullet. If there is copper in front of the burr, the bullet will not scrape off the burr, but will just pile up more copper.

You can tell that you have completed the break in when the barrel begins to clean up very easily. That absolutely cannot be predicted for any given number of shots. A top quality barrel such as a Shilen may take five or ten while a typical factory barrel could take a few dozen. Bottom line is, the barrel is broken in when it's broken in. Only the shooter can decide if it's worth the effort.