I can't see the break in the pic. EDIT: Oh, there it is... Even thought it looks like that part is under axial compression, it will still experience bending stress there.

Regardless, the rail on that one is *spring steel*, possibly different from standard rail which might be simply high strength steel. But any steel that is hardened, welding can be a big problem, unless post heat treated, or the material has sufficient "hardenability" that it rehardens from just air-cooling. Brazing might not reach sufficient temperature to be problematic. You need to talk to someone expert is joining pieces of spring steel, I don't know if this is possible.

New Brooks saddles are available as preconditioned, to eliminate long break-in time. I think that's your best and lowest cost option.