I've seen how it is possible to determine what a serial number is, even after it has been ground off (depending...).
Since material under the surface is affected--its structure compressed, and somewhat work-hardened--by the strike of a die, signs of what the number was will appear in miniscule relief upon the application of acid to a surface that appears to be flat and smooth. The process works similarly to how the relief between steel of two different hardness-es is brought out on Damascus steel barrels and blades. The harder of the materials will resist the acid's erosion more than the softer material adjacent to it.
What this would do to the area on the gun in question is anybody'e guess. You can at least kiss the finish goodbye. Another question is whether there is enough of the below-the-surface metal left to test. If enough steel has been removed, it will also contain this evidence. The edge profile on this one makes the last question relevant, since it appears to have undergone plenty of grinding to be in the shape it's in now., so it is a crap-shoot to look for the former markings in this way.
Whether the serial number's determination and restoration would be allowed by the Feds--or without a lot of hassle, if so--is a good question.
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"... Liberty is the seed and soil, the air and light, the dew and rain of progress, love and joy."-- Robert Greene Ingersoll 1894
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