SATA3 uses the same 'connector' as SATA2. Same as SATA1 even. The electronics on both ends, the computer and device differ though.
SATA 3 and all SATA' devices are considered 'backwards compatible', that is if you connected a SATA III hard drive to a computer that has SATA II built-in, the drive will only operated at the speed of SATA II level. In effect, you'd not get any better performance that you would with a SATA II device (and waste your money you paid extra to get SATA III).
I have a laptop with an sata II port. The cost of an sata III drive is the same now. So the real question is that if an older sata II drive will not max out a sata II port then will an sata III drive automatically max out the sata II port? Of course we are dealing with ssd's and the limitation is specific to the hardware and drivers.