No it doesn't. Those programs probably just check the SMART status of the drive. As a hardware tech, out of the probably hundred or so HDDs I've replaced... I could probably still count on one hand the number that have shown as failing via SMART.
I would say the symptoms fit that of a failing HDD. I'm betting that the boot time has slowed so gradually you haven't even noticed it. Since this is a PPC system, Apple retail stores will likely refuse to support it. It's also almost certainly on the Vintage list, if not Obsolete. So, check for a non-Apple retail AASP in your area, have them take a look. Might want to do it sooner rather than later, since that thing probably has a 2.5" IDE HDD, and those are getting harder to come by every day.
Of course this could be a golden opportunity to give yourself an excuse to upgrade. The new Mini models with Core i5 CPUs will be like a night and day comparison to what you have now. There's really no way to accurately reflect the performance difference you will see.