Re: 06 gsxr 600
Technically, you can run a stock bike and still be fine as a beginner/intermediate track rider.
However, there are things that make life easier on the track. The ease of replacement parts for rear sets and clip ons for example. So do you need anything? No, not really. But, having things like suspension and brakes will help you improve your lap times and tire wear/life.
If it were me, I would upgrade to an Öhlins FPK with the right springs for your weight and source a used rear (Öhlins, Elka, K-tech, etc.) shock. An upgraded master cylinder (Brembo, Accossato, Braking, etc.) with SS lines and race pads (Ferodo, Versah, etc.) will be the more beneficial than a QS, IMO.
At the end, it's not really what you're missing, it's what you feel is necessary in order to improve your technique, lap times, body position, etc.
Get yourself a red "R" and browse the classifieds, there are some nice parts for sale right now.