Can I activate a product key in UPlay for a game that I've already bought on Steam?
Solution 1:
As Steam and UPlay are totally different platforms and do't share the same account, there is no way, that each platform could know about the games on the other one. Therefore my answer is, that you can activate the base game on both platforms.
Also if that wouldn't be possible, then the game should automatically be in your UPlay library if you activate it on Steam.