The multimeter test will show if the cap is effectively open or shorted. If it acts "capacitor-ish", then you've got nuthin, because the multimeter test described will not tell you if your 108-130 uF capacitor is actually only 50 uF due to some problem. If you have the meter, and it's no big issue, then it might be worth doing as a "sanity check".
many multimeters do have an actual capacitance check range, though. There are faults that will not show up in that test, however.
If the circuit is acting like the cap is open, but the cap gives a reasonable response, then you know the real issue of the day is elsewhere. But you still do not know if the cap is in-spec. I have a nice little capacitance meter that came from "SUPCO", which does a good measurement, but not if the cap has one of those faults that can fool the meter..
It is worth just replacing in many cases, simply to avoid future hassles. But if you are not sure the new one is a good one, that changes the suggestion.