No, the registry doesn't appear in the secondary hull. Only in the saucer section. Having said that it doesn't appear like a kitbash ship to me.That's an interesting thought that hadn't quite occurred to me...a rebuilt starship. Maybe NCC-1031 was just the registry of the saucer they happened to get ahold of. (Or does it appear somewhere on the seondary hull?)
On another note, many have commented that the Discovery's saucer is similar to the Franklin's saucer. Personally I don't see it at all. To me the Discovery's saucer looks like an enlarged and widened Oberth-class saucer.