Not at all, it is so small you couldn't see them without a magnifying glass, these are micro etchings, little larger than the natural swirls the machine leaves when they bore the receiver out.
Given your premise, what prevents dirt from accumulating in these "micro etchings" obscuring the number?
As I stated, the only way for this to work would be to use deeper etchings that will affect the reliability of the weapon.
Oh, regardless, you would have to outlaw polishing your chamber as well.