Old receivers were (are) made of mild steel (think carbon alloy content below 0.4%). They will not through heat harden under any circumstance. They are easy to case harden and to get case colores on. The case, as mentioned, is very thin and contributes little, if anything useful, to deflection strength. All steel (all metal, for that matter) parts will act as a spring until their yield points are exceeded. Through hardened steel parts make springs that will stand more strain (think deflection) than soft steel. I doubt that the case layer will add anything to a steel part acting like a spring. However, the case will reduce wear on "bearing" parts/surfaces. And, it will add a lot to corrosion resistance (high carbon steel is much more corrosion resistant than is mild steel).
The parts we usually worry about wearing are the hook, hinge pin, barrel lugs/rib extensions, and bolt(s). These are not usually cased. The breach face and action knuckle might benefit from case layer wear resistance. However, both areas are low pressure and low speed bearings during action cycling that are easy to keep well lubed.
I believe it was/is somewhat common for Brit bespoke gun customers to take their new guns shooting before engraving and hardening to be sure they were satisfied while alterations were still relatively easy to make.
DDA
