You can stunt anything, but you'd prolly be very limited. The old cbr 600 F's weren't as popular as F2 and F3's so finding parts for them, stock or aftermarket, will be a little more difficult. You'd also be limted as the front tire is 110 and the rear only a 130. The engine only makes about 85hp from the crank so maybe 60 to the rear wheel, which isn't bad for an 88, but don't think you can go do a 2nd or 3rd gear stand up going 100+.
You could always increase the rear sprocket, but my advice is, unless your getting that bike for next to nothing, its really not worth the money to turn it into a stunt bike. You'd be better off finding a cheap F2,F3 or F4. Atleast you can find a pre-made crash cages for them and an abundant supply of cheap parts when you lay it down.