Yes, that’s a more precise description. For a given resolution and ISO, a larger sensor has larger pixels, which generally produce less noise than smaller ones.
Thinking about the individual pixels of a sensor is tempting but causes an unfortunate chain of erroneous assumptions.
It is true that (a) larger sensors have had an historical efficiency advantage, but it's progressively diminishing, and (b) larger sensors tend to be capable of lower area-equivalent ISOs. If you could build an MFT sensor capable of ISO 25, and used comparable glass, the full frame advantage would be eliminated.