Yes it does.. I once played a game on a Duel Sized map as Rameses II against Augustus Caesar..
Strangely enough both our capitals were seperated by only two tiles (Rome was on the end of that tiny peninsula, so it had no landconnection to the rest of the continent (the only one in the world). So, safe to say, I surrounded him as soon as I was able to establish more cities, then expanded from there, while constantly denying him open border agreements..
In the end, Rome simply collapsed due to the immense cultural pressure from three sides and I won the game. I can't remember what type of victory it was though, because I don't think I had achieved the specifics for a cultural victory yet.. Perhaps it was a domination or a conquest victory (even though no wars had taken place)..
So, in short, it is possible to culturally conquer the last remaining 'enemy' city..