Has the bbl been buffed/polished and then blued? Was it hot salt blued?
Does it need a bit of touch up polishing perhaps to take some dings,scars and dents out or remove some damage done to the edges of the flats.
I'd take the time to strip the old bluing off first and give it a little polishing up before browning it.
Vinegar (acidic acid) or diluted muriatic acid (hydrochloric) will strip the old blue off easily.
Then rinse the surface and dry.
Then I'd go over the bbl and polish it to even up the polish and remove any scars, dents, ect.
You don't have to get too fine a polish depending on the final effect of Brown finish you want of course.
I just feel if it's worth doing, take a bit of care and time and do it right. That way you don't ever have to make excuses for anything wrong with the final result.