As has been posted by others above, the short answer is 'No'. Old barrels may become unsound because they have rusted, because the lumps come loose or the ribs come detached or because they have been lapped too many times and are consequently thin. Obstructions may cause the tubes to bulge. All these things can be checked for.
Otherwise, damascus barrels are sound regardless of age. I spent the weekend shooting clays with a Manton double flintlock with damascus barrels, loaded exactly as Manton would have recommended when it was new. Shot 50 clays no problem. Likewise the 1840 Lancaster percussion muzzle loader we used the same way for 100 clays and the 1868 Sylven breech loader I use all the time.
I re-proof damascus barrelled guns regularly at the London Proof House and the Birmingham proof house. I have yet to have one fail nitro proof.
