depends how you want to finish it. If you are going to blue it, it might be tricky to get a proper match. Whatever metal you fill it with will more than likely be a different composition to the material of the action. Good chance they will blue slightly differently
Why be concerned by the stamping on the breech block?,as for attacking such a precise component with a mig welder .
I would tig weld it as the impurities from mig welding might make it stand out once blued.