There isn't a whole lot of barrel beyond the front sight base. This would be a factor in doing the machining. The bayonet, of course would not work if a brake was fitted. The front sight could be remounted further back on the barrel.
Probably the easiest way to set up the barrelled receiver in the lathe would be to grab the stripped receiver in the four jaw chuck, muzzle on the live center, and then indicate in the barrel to get the bore axis lined up.
Lots of SKS rifles at very reasonable prices - but I wouldn't alter one of the really nice ones this way.
I like brakes; they increase the shootability of most rifles.