My understanding of the strength of the spring is sort of along the lines of what OB said. However, as long as the steel spring is operating in the elastic region (not taking a permanent set), spring rate should not be affected by hardeness of the steel (making the steel harder won't make the spring stronger).
Peters, a modern coil spring is most commonly made from 1095 cold workhardened "musicwire". The process to make the wire aligns grain in a longitudinal direction. This wire is then cold wrapped on a mandrel to form the coil. So, IMO, if you heat the coil spring and quench it, it will allow grain reformation and not the in the longitudinal alignment of the original, therefore the spring will never perform to the level of it's original condition and not have the resistance to breaking of the original workhardened condition.
