The Seagate drive you mentioned is actually SATA II not SATA III (SATA III is 6Gbit/sec), but apart from the performance issues I mentioned in my first post, using a SATA II or SATA III hard drive on a SATA I controller does not affect reliability of the hard drive in any way.
Bearing in mind, of course, that drive reliability is dictated by the actual build-quality and reputation of the brand of hard drive you buy, nothing at all to do with the SATA controller it's connected to.
In my experience, for example, I've had nothing but trouble from Seagate drives, often failing in less than year, whereas Western Digital hard drives have performed consistently well and still giving me sterling performance.
Then again, other forum members may have quite the opposite opinion. I can only speak as I find.
That's not to say that WD drives never fail early on in their life, just nowhere near as often as Seagate ones. Again, that's my experience of them.