Rob,
Most of the bright, shiny stainless steel that you see at the hardware store has a minimum yield strength of about 30,000 psi. In contrast, mild steel bar stock, which is quite common, has a yield strength of 36,000 psi.
So, chances are that the stainless axle will not be as strong as the original one. However, it's impossible to confirm without knowing the mechanical properties of the original carbon steel axle and the proposed stainless axle.
Also, an axle with a yield strength of 30,000 psi may be perfectly acceptable from a design standpoint. For the most part, the Norton axle is subjected to shear stresses when loaded and these stresses are probably quite low. This would be easy to calculate if the dimenson of the axle and its supports are known.
Jason