How to make sure those heros come at the right time and that there is only one:

make the hero cost 255 population
make other unit upgrade to hero and preplace him somewhere
(make the other unit immobile or something, not available to any nation, the cost doesn't really matter, not even the pop cost)

Now you'll be able to upgrade the other unit to the "unique" unit and you are unable to build the hero unit :)
I tested it, and it works, you can start producing the hero unit, but it'll never get finished :)

Will the AI try and build it?

I'm pretty sure the AI will try to build the unit and get stuck with it.

Let's be serious here, is there anything which would have the same result AND be understandeable for the AI?

After some tests it seems that the AI isn't very keen on building them anyway, I made the warrior upgrade to swordsman and swordsman cost 255 pop and 1 shield, they didn't build any in over 40 cities for quite some turns, they only build archers and spearmen. And when I changed their production to swordsman, they would immediatly change it back.
But on the other hand, another civ with only one city kept building swordsman in that city.
The human player can build the unit however, but he needs to disband the city for it. (combined with making the unique unit cost 1000 shields, it's very unlikely that a human player would build it)

Thought it might be usefull in some scenarios...

I've had this idea before, but it's so hard to make something viable when the AI can mess it up...