Not a lawyer, but I'd think that without permission from the copyright holder you'd be in violation of copyright law. Serial number has nothing to do with it a builder (from legitimate plans) can use the plans number or not, as he chooses.

If you're just documenting unclear areas on the plans and you couldn't build a plane without also having the originals, that would be different... but getting approval from the copyright holder would still be the right thing to do.