A rogue elder brain certainly might, and others might be convinced it's a reasonable plan, at least for a while - but by the time the dead sun reached Severe status, it's likely that conventional illithid communities would consider the Brood to be of significant concern and the method too risky for the goal. Remember that illithids don't care for the Far Realm, and that while they love creating new crossbreeds and modified creatures, it's to serve as thralls - the uncontrolled and infectious Brood would be a source of particular alarm.