Is there a difference in the produced LUT, if, as augmented data, instead of a Grey Scale only I use a RGB primary ramp?
Assume the Grey Scale is same as the one in RGB primary plus the same primaries at 100%

Yes, as the additional RGB data will be used in the calculation for the grey scale Augment.
Grey scale data is never used in isolation, as that would potentially cause issues with artefacts/banding around the grey scale, as you can often see with the likes of Calman generated LUTs.

Steve