Engraving as a rule is done to the steel surfaces that are final finish Polished, but still 'In the White'.

When engraving is completed, a very careful final polish is usually given to clean up any small scratches accumulated through the engraving process. These from just handling the pieces and to remove any undesirable heavy burrs from the engravers cutting.
The latter should not be a regular issue if the engraver is sharpening his/her gravers correctly but the ocassional sharp burr will occur. Especially at the end of a cut.
You pick those up quickly by lightly swiping your fingers across the surface. Then pick those off level with a Flat graver as needed.

Any scratches and slight roughness in the cutting is removed with a careful polish with 1000grit or higher paper. Just a very light use, back and forth only a couple times will do it for you.
Anything further will start to dull the sharp image cuts and round them.

Off to be blued or plated.

Some pieces are left 'In the White' after engraving but that is not a thing that FActorys did. More of a custom engravers choice.
With care and maint, the surfaces do not suffer any more than a blued finish which needs all the same wipe down and constant oil/grease to remove fingerprints and such to keep it from rusting.

Engraving can be cut through Plating, but again it's not a common practice.
The last time it seems to have been a thing=to=do was in the 1970's.
Custom engravers were cutting through the Nickel plating on primarily S&W revolvers and leaving the bare steel cuts 'In the White'.
The slight difference in color was a very nice contrast.

A problem soon arose though. The nickel plating at the edges of the engraving cuts would start to loosen, flake and pull free.
This on guns that had been engraved in this manner that were not NIB when chosen for the engraving.

The NIB (unfired xcept for factory proof) did not have the plating delaminate at the cuts.
Used, fired specimens did and to different degrees.
So the fad of engrving thru the factory nickel plate kind of faded away.
I'm sure it's still done on occasion though.

Engraving thru the blue is also done. You see it mostly on inscriptions and names/dates added to guns. If the area is kept oiled, it won't suffer any more from rust than the surrounding blued surfaces.
I don't know if the Factory did 'Thru the Blue' engraving on small jobs like Initials, Monograms, dates, etc for customers sending a gun back in for the work.