The serial number on my carry gun is covered up by the grips, and the grips are not easy to remove.
Running the serial number without a warrant and w/o probable cause to suspect the gun is stolen is an illegal search -- but what are you going to do about it, call Eric Holder?
Nobody cares about your rights anymore, 1st, 2nd, 4th, 5th Amendment or otherwise. Because terr'rism and drugs and stuff.