Really, the only need for annealing and re-hardening a cut and welded receiver, would be if it had been welded back around the locking lugs, where it needs to hold its heat treatment. The receiver sees recoil energy, that it dissipates into the stock, but if it's welded correctly, say if cut at mid-ways the frame, I doubt annealing for stress relief is really needed, except for the instance above, or the base metal is known to be brittle, though we all still have it done. Of course, a lot has to do with selecting the right rod or wire for the weld, and how it's welded. I use 70 type wire, or 7018 rod, which is 70,000 psi, and try to not put a lot of heat into the base metal, by alternating sides. I've not tried it, on cut receivers, but I wouldn't doubt it if would not hold up.
4140, shouldn't need case hardening, unless for looks, since it's tensile strength is really high, and it's hardenable; with something like 95,000-120,000 psi tensile, according if it is hot or cold rolled, and annealed or not. The yield is not quite half that, which I think is about 60,000 to 75,000 psi. With a 2:1 safety factor, you're talking about 30,000 to 35,000 psi, to design around. If you harden and temper it, it really shoots up. One might even get by with a 1.5:1 safety factor, as it is used a lot.