Generally speaking, provenance adds interest and history to the firearm. It can also add value if one of the previous owners was a famous (not just wealthy) person such as a top tier actor (Clark Gable etc.), political figure (past president etc.) or a noted competitor or exhibition shooter (Annie Oakley etc.) or noted sports personality.
After seeing the pictures it appears your barrels are Vulcan, not Titanic. The circled V on the right barrel flat indicates Vulcan steel.
My BHE 20ga (originally Damascus ) was fitted with Vulcan steel barrels sometime in the mid 30's, probably by Remington/Parker as evidenced by Remington codes on the barrel flats.
Could you take another picture of the flat of the left barrel? That is where the repair codes are usually stamped.