Yes. All SATA systems are designed to negotiate between the controller on the mobo and the HDD, so they can agree on a communication speed and talk to each other. This is automatic - you should not have to do anything, It is supposed to just work.
The only exception I know about is a few early SATA I controllers could not accomplish this with new SATA II drives. But that was a very specific situation involving particular older controller chips, and NOT part of today's mobo hardware.