My motherboard is the Asus M5A78L-M, and I'm wondering if the Seagate 1TB Desktop SSHD SATA 6GB/s 64MB will have any advantage over a ordinary hard drive without SATA III, or if it will even work.
It will work and be slightly faster, SSHDs don't really need SATA 6Gpbs ports. The question is whether you need it to be faster, if it is your OS drive it will be more noticeable, but a separate SSD and HDD would be a better choice. If it is only a data drive, the performance will be less apparent.