Would that help dissolve the browning on it? I know that browning is a thicker and harder finish right?
It should.
From my understanding of bluing or browning, (and this isn't technical), it's really nothing more than a colorized rust treatment put on the gun is a systematic manor, and it gives a small amount of protection against rust. It takes several applications and removing, or carding, of browning or bluing to get it on evenly. The last act of bluing may be the application of a base to stop the acid etching of the metal, a wash with water, then an oil coat. Sometimes heat is added, to turn the brown to blue. But all of this is from my memory so that is suspect!
Bluing isn't a "hard coat' finish. If it were, then your gun would not rust, or scratch. I think of bluing as a process that fills in the pores of the metal that gives them some minor protection against rust. More than likely, your old gun was browned to keep the bare metal from flashing in the sun and scaring game, or to reduce glare on the barrel when sighting. Prevent rusting? No, or at best, very little. The old timers knew that after they used their gun, they needed to wipe it down with something greasy or oily to protect one of their major investments. Just as they knew that after they worked their horse, they needed to cool it down before it was put away.
Vinegar will remove the coloring back down to the metal, with perhaps some minor etching of the metal.
BEFORE YOU DO ANYTHING, how about showing us a picture? Anything you do may reduce it's value.......