I've done this (cultural victory), on Deity, with one military unit the entire game (a war elephant). Either that was one intimidating elephant, or AIs don't automatically DoW you if you can't defend yourself. I got involved in a few pacts of cooperation, but no pacts of secrecy or defensive pacts, and I kept my empire very small.
Civs demanded gifts from me a couple of times (which I gave them), and they often asked me to get involved in their wars (which I gave the polite refusal), but they never got angry with me for any reason that I could see, and many of them even asked for open borders with me (which I gave) so they could move through my territory to fight each other.
Yeah but I'd like to play one where if a Civ next to me starts getting uppity, I can bribe another civ to war with them, etc. Would be awesome. A truly diplomatic game. Not sure if it's possible. Might try tonight. Basically keep the other civs in check, whenever one starts getting large, bribe the others to war with them.