I have already contacted SE regarding this concern, and this is the exact response I've received from Tim Post, an SE community manager (important points bolded by me):
To the extent that it doesn't at all annoy others in chat, we tolerate
it. Bots shouldn't send automatic greetings, say inappropriate things
(or accept inappropriately named commands) and should not be used to
do anything that someone couldn't ordinarily do with their account.
They're also subject to plug-pulling at our discretion if we feel that
they are in any way creating a problem; for us, or other participants
Technical caveats include not being upset if we change something about
the internal-but-really-exposed-sort-of chat API, how authentication
works, adding human verification, etc - we're not going to heavily
consider third party clients when making decisions about changes we
need to make. There's also no support for bots in chat - though devs
involved with chat will generally try to be helpful if you're working
on something neat. Still, it's not something we support.
However, someone that has something rather benign running in a room
doesn't have anything to worry about, so long as they're keeping an
eye on it. Additionally, in most cases, the strongest action we'd take
is kick the bot out of the room and ask the owner to disable it. If
someone was being intentionally malicious with one, we'd definitely
take a stronger action, but the bot becomes incidental in that case.
As you can tell it's a bit of a gray area, but not taboo. A few folks
started working on a bridge between IRC and our chat system, I'm not
sure what came of that. I'm inclined to say let's see what comes of