I don't know if SS can be browned, but it has been "blued," or more correctly known as "Black Oxide" coated for many decades. Prior to immersion into the 285 degree Black Oxide solution tanks, it has to have the surface "striked" by immersion into mild acid. We did this by immersion into common "Brick Layer's Acid" or Muriatic Acid for about 20 seconds followed by a dip in boiling water to stop the Acid from further action. Then it went into the cleaning solution tank and finally into the Black Oxide Tank. After it was immersed long enough, it went into another solution to stop the Black Oxide from working and finally into a "Rust Veto" or anti rusting solution. Done properly this did not hurt the super accuracy of NM or Sniper Barrels at all.
So it won't hurt the inside of a ML barrel AS LONG AS the breech plug is done separately. If the breech plug is left on the barrel, the Black Oxide salts may not be properly neutralized in the threads of the breech plug or barrel, unless one is very, VERY careful. That leads to a white powdery bleed out of the salts, that will eat the finish underneath and ruin the finish.
I do not know if the careful and short applications of Muriatic Acid on just the outside surface of the barrel will or even can cause an even enough surface rust that can be carded like browning. Honestly, I would never try it even as much as I've worked with Muriatic Acid on the barrels mentioned above.
Now SS can be painted or plated or other more expensive treatments can be done, but I doubt it will look like what we call "browning."
Gus