No, the top cover would not be allowed. The manufacturer must be on the receiver or barrel (info from ATF site below.)
As far as no one noticing, I really wouldn't want to take the chance.
ATF Info on marking Weapons:
Sec. 179.102 How must firearms be identified?
(a) You, as a manufacturer, importer, or maker of a firearm, must legibly identify the firearm as follows:
(1) By engraving, casting, stamping (impressing), or otherwiseconspicuously placing or causing to be engraved, cast, stamped (impressed) or placed on the frame or receiver thereof an individual serial number. The serial number must be placed in a manner not susceptible of being readily obliterated, altered, or removed, and must not duplicate any serial number placed by you on any other firearm. For firearms manufactured on and after [insert effective date of final rule], the engraving, casting, or stamping (impressing) of the serial number must be to a minimum depth of .005 inch and in a print size no smaller than 3/32 inch; and
(2) By engraving, casting, stamping (impressing), or otherwise conspicuously placing or causing to be engraved, cast, stamped (impressed), or placed on the frame, receiver, or barrel thereof certain additional information. This information must be placed in a manner not susceptible of being readily obliterated, altered or removed. For firearms manufactured on and after [Insert effective date of final rule], the engraving , casting, or stamping (impressing) of this information must be to a minimum depth of .005 inch. The additional information includes:
(i) The model, if such designation has been made;
(ii) The caliber or gauge;
(iii) Your name (or recognized abbreviation) and also, when applicable, the name of the foreign manufacturer or maker;
(iv) In the case of a domestically made firearm, the city and State (or recognized abbreviation thereof) where you as the manufacturer maintain your place of business, or where you, as the maker, made the firearm; and
(v) In the case of an imported firearm, the name of the country in which it was manufactured and the city and State (or recognized abbreviation thereof) where you as the importer maintain your place of business.
(b) The Director may authorize other means of identification upon receipt of a letter application from you, submitted in duplicate, showing that such other identification is reasonable and will not hinder the effective administration of this part.
(c) In the case of a destructive device, the Director may authorize other means of identifying that weapon upon receipt of a letter application you, submitted in duplicate, showing that engraving, casting, or stamping (impressing) such a weapon would be dangerous or impracticable.
(d) A firearm frame or receiver that is not a component part of a complete weapon at the time it is sold, shipped, or otherwise disposed of by you must be identified as required by this section.
(e)(1) Any part defined as a machine gun, muffler, or silencer for the purposes of this part that is not a component part of a complete firearm at the time it is sold, shipped, or otherwise disposed of by you must be identified as required by this section.
(2) The Director may authorize other means of identification of parts defined as machine guns other than frames or receivers and parts defined as mufflers or silencers upon receipt of a letter application from you, submitted in duplicate, showing that such other identification is reasonable and will not hinder the effective administration of this part.
Signed: April 12, 1999