I'm not an expert in steel, but have done quite some work in flow properties of materials and would just echo some of the posts concerning linear and non-linear phenomena.
The drive shaft will experience torsional stress as it transmits the power from the engine to the wheel (and under braking in the opposite direction), the magnitude of which will depend upon the torque transmitted from the gearbox and the limit of adhesion of the tyre.
The degree of twist in the shaft will be a function of the lengtrh of the shaft and the Youngs modulus (limiting stiffness) of the shaft. Assuming the torque applied is below the Youngs modulus any deformation should be elastic, and therefore recoverable. It is evident from the pictures earlierr in this thread, that there is also some permanent deformation occuring in those shafts. This implies non-linear behaviour (i.e. that the stress/strain ratio is not constant at large stresses).
I think the mild steel and titanium, comparison was a good one to illiustrate the difference between modulus and strain. Given that the strain in the driveshaft, provided it is in the linear range, will be proportional to shaft length it follows that a longer shaft will twist more than a shorter on for a given percentage.
Non-linear phenomena, such as fatigue, are very tricky to model and introduce the problem of trying to predict when a component might fail. As PhilipM also mentioned, there is the complicating factor of non-torsional stresses (bending, as opposed to twisting) as the car goes over kerbs.
I quite like the idea of using spring steel as a drive shaft, I have visions of elastic band racers! although my sense is that it would be better to have a very stiff shaft and keep the strains within the linear range. I suspect this is the reason teams tend towards a larger diameter, hollow shaft than a smaller diameter solid one, and make it from a very stiff (high modulus) metal. I still maintain that they btyre will be the lowest stiffness material in the drive train and should undergo the largest strains as the power is delivered.