I don't know what welding would do to the strength of a frame back then. I don't believe guns were heat treated during manufacture when that TL's frame was made, nor what steel alloys were used. If low carbon steel, it couldn't have been heat treated anyway.
True that it would not have been heat treated originally, but after welding it WILL have weld induced stress.This could be dealt with by heating the frame up to around 900 f, holding it there for a period of time (dependent on thickness)and then slowly cooling it over a period of about 12 or more hours. If the gun was used to fire rounds in the 14000k range as originally designed it probably wouldn't matter one way or the other.
Plus, low carbon steel can and is often heat treated. It will not harden to any degree, but there is a LOT more to heat treating than hardening to form martensite. Harding is only one type or procedure of heat treatment, annealing and stress relieving, resetting the grain and tempering are other types of heat treat. There is a lot of low carbon welded pressure piping that gets stress relieved.
It is my belief that one of the refinements in S&W heat treatment had to be a step to reset the grain after forging. Forging needs to occur at temps over 1600 f and that kind of temperature will cause grain growth. Larger grain structure is more brittle than smaller grain structure.
A hardening and tempering cycle without resetting the grain would result in a inferior steel structure. S&W frames and cylinders are not hard. Actually about the same hardness as mild steel. It is all in how they got to that hardness. Soft fine grained martensite is way tougher than soft pearlite. Tough and hard are not tthe same either. Hardly.
Forged in fire is an interesting show, but they never show or discuss resetting the grain or the tempering cycle. Any blade made without these steps is going to suffer failure. Without tempering they would all break on impact testing. A fully hardened blade before tempering will often shatter just dropping it on the floor. I once had a piece snap just sitting it down on an anvil.
There are tons of myths, misunderstandings, etc about steel, its properties and especially about heat treatment.
Here is one. File steel is brittle. LOL, same steel is used to make cable like used on cranes. Difference? Heat treatment.