Will KILZ® contain black mold?
It has been proven in recent years that chlorine (bleach) does not kill mold, especially on porous surfaces.  It hurts it a bit, but really just bleaches it out so you don't see it.  That's why it comes back so quickly. The mold remediation industry no longer uses it and strongly advises against it. Here's one site (I just googled, do not know these people):
http://www.countyservicesinc.com/bleach-myth.php

Sheet rock is one of mold's favorite foods and is quite porous - so if there is mold in a piece, it should be replaced.  Kilz might contain it on other surfaces, but it will grow inside sheetrock and can spread to an area that isn't Kilz'ed, so I'd say "no" in this instance.  

Also, in reference to James's statement ... chlorine does kill bacteria - but mold is a fungus.