Probably not. Breakout has 240 rear , especially the rear downpipe "kicks out" more.
Breakout mufflers are like Heritage/Softail custom mounting bolts/brackets , again different from Fatboy
Aha so it does "fit". My experience is all of trying to retrofit the "other way" , 200/narrow rear system onto a 240 rear and that no way works..not without engineering input !
I had to compliance a couple of 2009 CVO Springers a few years back and no stock Softail 180/200 rear systems fitted ( first/second model/year of the 240 rear you see !)
In those cases I used a Rocker stock system ( 240 rear !) , downpipes and mufflers. Still got that in the shed "for later" haha..
EDIT watch out for the different O2 sensors across the model years , both size and location . That alone may make it "too hard basket"
It would for me anyways. 2011 the O2 sensors changed so Breakout and 2012 Fatboy should be OK and good to go