Inquisitor,
An ACAS II equipped fast-jet may well get RAs caused by it's own high rates of climb and descent. Equally though, non-ACAS fast-jets squawking Mode C are unknowingly triggering RAs in other traffic, which is why they have been asked to limit their manoeuvres to 8000fpm when near controlled airspace.
An ACAS II fit in a front-line fast-jet would have it's full utility reduced by being set to 'TA Only' whenever the aircraft was operating as part of a formation, which would be most of the time.