Leaverbuster is active for any matchmade game, which includes Co-op vs. AI. The only matches Leaverbuster isn't active are custom matches.
Also, Leaverbuster has to treat all leaves equally, otherwise it would be way too easy to trick it into thinking you left because your power/internet went out when you actually intentionally shut off your router to leave.
That being said, Riot does know that sometimes stuff happens that causes us to leave a game, so they designed Leaverbuster with some leniency. You don't get punished for one or two occasional leaves, you get punished when you use up that leniency by showing a pattern of leaving multiple games. You stated that you have the 20 minute punishment, which means that you have been punished by Leaverbuster before, as that is not given out as a first time punishment. You need to have gone through at least 2 other punishments beforehand. This also means that you have definitely shown a pattern of leaving multiple games in the past, so unfortunately for you, you have already used up the built-in leniency Leaverbuster has, and leave now could very well trigger another punishment.
I know this doesn't seem fair, and to be honest it isn't too fair at all, but Riot has to punish frequent leavers regardless of the reason, otherwise, like I said before, it would be to easy to make it look like your power went out to avoid any sort of punishment.
