Traditional slow rust blacking or browning of Damascus barrels should do nothing to harm the integrity of the barrels or the rib soldering joints. It is hot caustic salts bluing that is detrimental to soft soldered double barrels.
Many barrels have less than 100% solder joints, and some water or etching solution may get inside during the boiling, etching, or rinsing process. The rusting solution is typically put on very sparingly, and should not get inside. Many people think drilling a weep hole to flush the area between the ribs and barrels is a good idea. It doesn't hurt anything, except providing a clue that the barrels have been refinished. But simply doing a good neutralization and rinse, and then drying the barrels in a very warm place will vaporize and drive out any traces of moisture within. That entire area is typically well tinned during soldering, so worries about unseen corrosion continuing after refinishing are overblown in my opinion.
