From what I've seen, it is possible for the AI to
change its mind on who it's plotting on, or whether to plot at all, but there's no garuantee.
Quite often while I'm at war with AI X, another AI, (Y) will start plotting, and Y is not in any wars currently. However, if I capitulate or make peace with AI X, Y will often immediately stop plotting.
Another time I've seen Hatshepsut next to me at cautious plot on me (stack of units in city next to me, and has the fist of death). I Switch into her religion and make her pleased, and beg gold. Couple turns later she stops plotting.
Begging gold doesn't seem to do anything, it just prevents them from DoWing for 10 turns. You can use this time to make them pleased/friendly which
can get them to stop plotting (if it's on you), bribe another AI to attack them, which will completely screw up their plotting plans, or build a big enough empire and military to scare them away.
Likewise if they refuse gold when you beg, it doesn't mean that they're plotting on you, it just means they're being stingy. If you have known an AI for a while (50 turns plus) and they are at pleased and you haven't begged, they should ALWAYS say yes the first time for 50 gold~.
However, if you are at a peace treaty, and then the AI begins plotting while you have several turns left, you can be sure it's not on you, unless you refuse a demand after your peace treaty expires.
Another interesting situation I had on one of my games was Julius ceasar was in a war with Shaka, then decided to demand something off me. I said no because I was sure to be safe, he didn't even have any units near me. A few turns later, while he's sitll at war with Shaka, he declared on me and sent one catapult to invade.

Some AI like Montezuuma are crazy enough to immediately declare on you while already at war if you refuse their demands.