But, and this is the important question none of you have answered yet, how would this be any better than the current AI? How much work would you have to put into training the AI before you have a set of seeds that can cover the same amount of configurability that the current AI has?
In the end, the difference between a neural-net-driven AI and a normal procedural one is something the end user is probably never ever going to notice. So the other important question is, why bother?
My proposal was to create a plugin for an entirely alternate AI system, one built using genetic coding (a form of genetic algorithm evolution). Theoretically you could accomplish this by mapping function building blocks (either in Lua or C++) to "genes", then mutating them in certain ways to evolve a certain AI behavior (attack, evade, etc.)
You would need a "fitness function" to determine the suitability of each "chromosome", but this could be tied to such things as hull strength and length of time before getting destroyed. You would also need to add a hook into FreeSpace to run a mission with this AI over and over and over... for long periods of time. Possibly weeks. Possibly even months. However, if this had been started when I proposed it, two years ago, we could have had something by now.

Upon reflection, this may actually be somewhat different from what the original poster was asking about.