This alloy can have a variety of heat treatments applied: Process anneal, full anneal and of course hardened and temper.
However, normalizing is not recommended for this alloy. Why not?
Normalizing , air cooling, is the same as a quench for 13 Cr . Quench without temper is likely to give low toughness. I usually sub-critical annealed to soften it because a full anneal requires hours to cool to 1000 F.
Do you mean normalization alone? Obviously without the temper, you will lose your toughness and corrosion.
If you mean the cooling rate, air cool vs oil or water cool, normalizing may give you insufficient cooling rate to get full martensitic for a large cross section, then slower cool will give you some grain boundary carbide leading to intergranular corrosion. this can worsen the effect of H2 embrittlement.
being said, normalization can sometimes be used for grain refinement.