Yes, this is the heart of the repair. Yhliem is right on about the metallurgical changes that take place. It doesn't matter how quick to welder is, as whats more important is how quick it cools.
In a weld every form of heat treating takes place from the hardening of rapidly quenched martensitic transformation to the annealing properties of a slow treatment. Hard and brittle to soft and pliable. But as csnow points out, metal is cheap and structural reinforcing from the adding of material to the thickening of the fractured area can easily make the end result stronger than the original clean sheet.
Bosch Master, ASE Master, L1
33 years MB technician