Kawasaki released a factory turbo version of the GPZ in the 80's. It had a 750cc engine but quite a small turbo. A common upgrade is the T2 off an ET Pulsar, so I would suggest that the sizing would be reasonable for your GSXR600 at a low boost level. Remember that motorbikes run very high compression and ambitious timing to make the power that they do.
That said, for better response (given that the 600's are already quite 'top endy') you may want to look at a ball bearing turbo. I believe that Garrett have a flavour of their GT ball bearing turbos that would suit your motor - I think they go as small as 200hp. Don't quote me on that, you'll have to speak to a turbo shop.
If you're looking for advice on bike turbo conversions, you can't go past S&R Pro who have a number of turbo bikes (mostly Suzukis) and plenty of experience. They do ride in-ride out conversions for about $10k on injected sportsbikes. Depending on what year your motor is it may be carb'd, which means it would be MUCH cheaper, probably around $3k depending on what turbo you chose.
At the end of the day though, it would probably be easier and cheaper to trade up to a GSXR750/1000 and be done with it. From memory the 05 thou's have something phenomenal like 165rwhp and weigh 168kg... but you can get onto an 02/03 model for about $12k, and about half that after your trade-in (depending on model). Worth a thought.. but I know it's not as cool as a turbo bike