And any decent meter would have a CAT rating. (Except, of course, those made before the CAT rating system was invented. In that case, a used meter made by a trusted company like Fluke or HP would still be good. But check to make sure the previous owner didn't just bypass the fuses!) Also beware that the cheap multimeters generally use glass fuses (low breaking capacity) or no fuse at all. If you accidentally connect that meter set to amps across a supply capable of a lot of amps (car battery or even a large PC PSU), the fuse might simply arc through like a welding torch instead of properly blowing. Some higher end Fluke meters would beep if the probe is left in the current jack when set for voltage and the Gossens would even prevent you from turning the knob to voltage unless you first remove the probes.
Good point about the power coming through the PCIe slot, I work at a company that makes server network cards and they use special interposers with built in shunts (shunt directly on the interposer = minimal resistance) and some networkable Agilent multimeters to measure power. But even a high end network card uses very little power compared to even a low end GPU. A modern GPU is going to draw most of its power from the 6 pin or 8 pin connectors.