Brimstoner, when you manufacture steel, weld, etc, you create martensitic regions etc in the heat affected zones, normalizing is to remove these microstructure "imperfections", then you would slowly cool the microstrucutre to allow time for the grain boundaries to become uniform (as you said this results in a much finer grain in the microstructure) which increases strength of the material.
Stanweld, I misread, I understand it is not Gr B 5L pipe, but you should not be using A53 Gr A for most piping applications.
As far as grade of of material, these materials are good mettalurgical replacements, however neither are recommended for 36" pipe per ASTM.