The fan clutches were notorious for failures until a 2005 redesign. Then they got better. GM also updated the PCM software to force the fan to engage right after a start where the cabin was hot but the engine coolant was not, to get the cabin cooled off faster. But if the fan clutch was not spinning at the commanded RPM, you would most likely have a Service Engine Soon light and a code to read to confirm the failure.
If the AC performance is getting worse on a 2002, I'd get the pressures checked since a slow leak is more likely than a bad fan clutch. Or debris in the condenser or radiator fins.
A high end scan tool can read the actual fan RPM versus the commanded fan RPM and tell if the clutch is really bad.