I said nope, I'd use some generic system, but that got me to thinking:
Most licensed games would probably be better off if they were written like The Pirate's Guide to Freeport - systemless, but providing all of the information you need to actually run a game there using whatever system you prefer. Then, you produce system-specific supplements which stat out NPCs, translate setting concepts into feats/magic/prestige classes, et cetera, according to the prospective market for each system.
A systemless setting book is just as good as a "proper" licensed RPG for the franchise-fans who will buy the book for the sake of the information it contains on the franchise - I still think most of the people who bought Serenity aren't playing games with it right now, and I know that about half of the people I know personally who bought the game never intended to play it - they just wanted more information on the Firefly 'verse.
In a way, it would be like those encyclopedias and visual companions for high-profile properties like The Lord of the Rings, Star Trek, and Star Wars - it would certainly have a lot more crossover appeal for seeming like a guide to the world of the game than an actual separate game you'd have to learn to play, and I don't think that being written like a systemless roleplaying setting would really harm it on the "setting bible" front.
This crossover, mass-market appeal might help to mitigate the costs of selling at least two separate books before you can actually play a game in the setting - although, of course, plenty of people who do intend to game with the systemless book will be planning on doing the mechanical work themselves, anyway. Again, I know of people who own Serenity purely as a setting bible for their GURPS or Traveller games.