Radiator cap pressure varied for various Triumphs and across various years. Lowest I know of is TR2-early TR4 with 4 psi nominal. Highest I know of is late Stag (and maybe TR7 ?) with 20 psi.
Early TR6 was 7 psi, later TR6 was 13 psi.
Adding a recovery system to a system not originally so equipped probably would increase stress on the radiator *very* slightly, since the radiator will see slightly more vacuum when it has to lift the water up from the level of the recovery bottle. But this is trivial compared to the pressure differential it sees in normal operation anyway, so I can't see it as being a problem.
BTW, late Stags have the pressurized bottle as Geo mentioned. I now have one of each, since my second Stag has been converted to the later cooling system.