No, it does not take 4 weeks for the lye to neutralize!
The chemical reaction between the base (lye) and acids (oils) is exothermic ... it gives off it's own heat. When the soap gels, you are seeing the chemical reaction in action! When I started making soap in '99, we were told to insulate the soap and not peek for 24 hours! The insulation was to keep the heat in to give you a full gel to the edges of your soap (And it is perfectly fine to peek!)
I've measured temperatures in my gelling soap at over 180*F. This was only a few hours after the soap had been put in the molds. When your soap has cooled down, saponification is complete and the soap is safe to use at that time.
CPOP is just another form of insulated CP soap where you give the gelling process a boost of initial heat.
Yes, using the HP method you will have completed soap within a few hours, but you still need to mold it and let the soap cool down in the mold. With the CP method, you will have to wait until the next day until the saponification has completed.
For folks that retard the exothermic reaction during soaping (by not allowing the soap to gel), I wouldn't venture to guess how long it takes for the lye to neutralize.