Welcome to the community, renegade682!
Yes, you can use a SATA III HDD in your motherboard's SATA II ports. It doesn't really make a difference for mechanical hard drives. A SATA III (6Gb/s) port is required if you are planning to use an SSD for example, mostly because a SATA II (3Gb/s) port would bottleneck the speed and performance of the solid-state drive.
In your case, I don't think you'd have anything to worry about. The WD HDD you are planning to upgrade your storage with should deliver the same read/write speeds, regardless of whether or not it's connected to a 3Gb/s or a 6Gb/s SATA port.
Hope this helps.
SuperSoph_WD