I ran a test and the following notifications are sent when Siri appears:
_UIApplicationWillAddDeactivationReasonNotification
UIApplicationWillResignActiveNotification
... and when Siri is dismissed:
_UIApplicationDidRemoveDeactivationReasonNotification
UIApplicationDidBecomeActiveNotification
So, no... since there isn't a public Siri API, and UIApplication doesn't send any Siri specific notifications, it looks like we're out of luck for now.