Midgardsormr
Warlord
Firaxis does not really want the AI to win per se, they want the AI to play make believe, ie act like the personality of the civ leader. The purpose of the AI in civ6 is simply to give the player a "big personality" to interact with so that they are not playing by themselves.
The trained neural net wouldn't necessarily have to be the only AI system. The current AI could be used for policy decisions—when to go to war, which cities to attack, what VC to pursue, how to respond to player actions; and a neural net could be used for combat decisions, which aren't generally influenced by leader personality, anyway. And the combat system has far fewer variables than the overall game, so training the AI would be inexpensive in comparison to building one that would play the entire game. Maybe still more expensive than Firaxis might be open too, but not as costly as training on the entire game. It would probably be quite an overhaul of the game, though—getting a neural net to play a game is an entirely different thing from building it into the distributable code.
As previously mentioned, a neural net could be trained to a specified level of competence then halted. It might even be possible to train several on different games, resulting in multiple different play-styles that could be assigned to different civs, or perhaps randomized, so the player wouldn't immediately be able to guess what strategy the AI would use.