Does fertilization finish before the conceive date of pregnancy?

Yes: Fertilization is conception. Therefore, a woman whose egg has finished being fertilized has finished conceiving. She has a one-celled "baby" which is just a fertilized egg. It splits into 2 cells, then 4 cells, then 8 cells, etc... No woman knows exactly when she conceives, in a natural pregnancy. How would she know? She can neither see it or feel it. Conception dates are therefore only estimates.