Playing as Egypt I got a Khan GG (with 5 movement) from a city state because I had the Educated Elite Policy recently. It was later game and I was playing for Culture, but I tell you, when I got that Khan it was super tempting to rush to tanks and go on a high-speed late game conquering spree. But I was so close to a culture win that I decided to forget about it and just replaced my current GG with the Khan.
I've gotten several UUs when I've had a military City state.
On the downside, I've also received the regular unit from a city state when playing a civ that had a UU.
I've never seen it, but I can imagine I'd be a little disappointed to find myself in a war with another civ that was attacking me with my own UNIQUE unit. Just seems like nonsense to me.
Ok, that's different: One thing are Great People (that is from culture) and another one are units
I got a Khan from Brussels in my last game (I was Greece). Sadly at the time Brussels was completely surrounded by Mongols, who killed my Khan before he could get to safety.
I usually seem to get Great Engineers from Educated Elite - which is fine, but if I want a building or Wonder rushed, it can be a little irritating that they often take longer to get back to my territory than the building takes to complete...
The last thread about this had a screen shot with the player (France) attacking Germany and German Foreign Legions. It's not a big deal, I just think they can do better.
I don't think we can see this. A unique UU will appear only if the civ related to this UU is not in the game. Maybe i'm wrong.