I've been thinking about it a lot and there's something seriously off in this "prevention-based" approach to political correctness.
People can get offended at all sorts of things. Maybe some girls will be offended at people saying "guys" gender-neutrally. A lot of women won't.
Are you going to write bots to prevent all possible verbal offences? What if some of those bots offend people themselves, what do you do then?
I find it interesting you mention the nondiscriminatory aspect of a bot as a feature. To me it's one of the most disturbing parts, and it's what creates the "passive aggressiveness" I was talking about. If you have a problem with the way I say something, you can be upfront about it with me and I'll change my behaviour. Writing a bot for it is quite a backhanded way of getting me to do something, with less chances of succeeding (and if anything, more chances of continuing out of spite).
Like I said though, all this is personal take. Maybe everybody at your company is fine with this. However, I did show this little post around and got a near-unanimous reaction similar to mine, which reinforces what I thought before: It is highly likely there's people at your company who think this is far more than "a silly nudge", and the bot would then have a completely counter-productive effect to its original intent.