Yikes! This may seem easy to say in retrospect, but I've worked at large orgs where I've had to give public demos or keynotes. If I wasn't giving the demo in a completely different logged in user/profile for some reason, one of the first things I'd check before going in front of people was that every app that wasn't specifically required for the demo had been shut down and that all notifications and alerts had been turned off/snoozed.
Hopefully this makes it into some company-wide training and standard so there's not a repeat in the future.