Just changed from a 120/70/17 207rr to a 120/60/17 on my ZX6R track bike and makes it turn in that little bit nicer, so the only problem you may have is it will turn in slightly slower and also the tyre may catch the front mudguard

Fitting the higher 70 profile tyre will make it more stable but with the 'slowing' up of the steering as above.