I guess it depends on what exactly is meant by "broken in". I found it pretty comfortable right out of the box, but then it seems to get more comfortable as time goes by. When does the breaking in stop and the breaking down start? Hard to say, but I would say that my saddle got progressively more comfortable throughout the first 4000 miles.
I don't think they ever stop breaking in... That said, what is "breaking in".
You buy a new saddle. Once you start riding, your pelvic bones hammer away at the saddle until dips start form that match your pelvic bones. Your left pelvic bone is slightly bigger, so it works longer to create a bigger dip. Those dips form because the leather stretches in response to your body's protrusions. As you get older and your protrusions change, the leather continues to stretch and adapt to fit you.
The saddles have tension mechanisms because of stretch too, and that is still technically "breaking in". As long as you can apply tension, the saddle is still useful. When there is too much stretch, we retire the saddle. Brooks is generous with their leather choices, so over stretch does not happen too often.