Hi Andy,
Welcome to Tom's Hardware!
Yes your SATA III HDD will work in the SATA I port, just at the SATA I 150 MB/s speed. Some of the older SATA II cards had a jumper to set for the slower speed but I doubt that your newer HDD has to be manually set on the back.
Later, when you upgrade to a faster MB with SATA III ports, your HDD will run at native speed, without a handicap!