Top Gun has evolved a lot, it now has air-to-air, air-to-ground and CAS in the syllabus. And I'm not sure how the CCS course helps with commanding a squadron as for that you have various leadership courses at the Air War College....as I know a couple of who commanded squadrons without ever going through CCS (distant relative was a former Mirage OC and now OC Flying on JF-17s).
CCS always had two dedicated squadrons, often taking the roles of aggressors. Mirages and F-6s (now F-7s) were the two main squadrons, and now a JF-17 squadron is also there, not sure if they're used in aggressor role but definitely in DACT. Yet CCS units can be deployed and utilised for combat if needed......years ago during Gulf War I, No. 14 Squadron on F-16s and a CCS Mirage squadron were given orders to get ready for Desert Storm deployment to the Middle East.....shortly after the orders were revoked.