Rick Sternbach has stated that the desktop model was always meant to represent Picard's previous command (The Stargazer), although ironically it was quickly replaced by an AMT Enterprise-A model for "The Battle" when the possibility existed that a new filming model wouldn't be ready in time and they might have had to reuse the TMP Enterprise for the Stargazer. Luckily that didn't happen.
I read that the reason the model was pulled from the ready room set was so it could be used as a reference for Jein's team to construct the Stargazer filming model. In one scene, Levar Burton does say "Constitution" class, so they were planning on using the movie model, but couldn't get it or something, so they decided to build the model based on the kitbash, and then dub over that line with "Constellation".
I've studied that kitbash model, and it's really neat. A couple of AMT Enterprise kits, pieces from a Gundam kit, pieces from a Battleship Yamato kit, and other various Anime model pieces. I was able to find the exact model kits used, and buy them along with a vacuuform kit of the Stargazer in my closet (same scale as the ready room model), which I hope to build someday.