Levels do matter b/c they test different skills.
AA is where young pitcher face hitters who can hit ML fastballs on a regular basis - you can't just throw it down the middle of the plate and expect good results.
AAA is where you start facing a lot of hitters who will spit on secondary stuff out of the zone and get you behind in the count - they may not be able to hit a ML slider, but they're experienced enough not to try if it's out of the zone.
You can rush a guy in a relief role if he has a plus FB and one average secondary pitch - at least in a middle inning role. But is that good for development?