As a moderator who spends a lot of time on chat...
It depends. Practically speaking, while bots theoretically have one owner, many bots are maintained by multiple members of the community. The point of a suspension isn't just punishment - it's to let the user have a timeout when they misbehave. I suppose part of the issue is "does suspending the bot do this?" and whether it is collective punishment, and is leaving the bot alone against the spirit of the suspension?
Historically, and rather interestingly - the chat bot on Root Access was suspended, and not the maintainers, so there's some degree of precedent for a bot being suspended for not acting correctly, but not the owner - and presumably that can work the other way.
Considering that we have taken a dim view of people trying to get a chat bot suspended in the past (though I can't remember enough to pull up an example), if a bot is triggered to perform an action that's against the rules, we'd have to review both the bot and the person who triggered said action.
On the other hand, on Root Access or any other chat room on which I am a regular, I'd totally kick someone who's clearly trying to get around a suspension with a second account. The utility of the bot to the room and the lack of use to get around a suspension is critical here.
So, assuming that the bot continues to serve its purpose in the community, the maintainer doesn't use it to get around their chat suspension (and this would/should result in increased suspensions for the user and presumably invoking the "this is why we can't have nice things" rule), I don't see any particular benefit in extending an owner's suspension to the bot automatically.
Where abuse occurs, of course, we'd need to review and use common sense, in mitigating the abuse.