My understanding of the definition of the liquid limit is the moisture content at which the material acts like a liquid and not a solid. I think the difficulty in having confidence in the value is that materials which are non-plastic, often don't behave in a predictable manner when you test them for the liquid limit. I am speaking here specifically about when you use the cone penetrometer, as a material becomes less plastic, they become more susceptible to what I have always called dilatency (although I stand to be corrected for using the wrong term, what I mean by dilatency is that when you shake a silt, the water rises to the surface, we always called this dilatency in the army, and I can't get out of the habit now - sorry).
Anyway going back to non-plastic soils (fines passing the 425µm sieve)you can measure a 'liquid limit' but in my opinion the results will be very difficult to accurately reproduce. This is because any vibration/knocking/tapping of the sample effects its structure, the excess water required to 'liquify' the solids is rapidly released and the solids 'settle'. Water comes to the surface, and the solids are effectively compacted, thus reducing the penetration of the cone thus reducing the liquid limit for the smae 'overall' moisutre content.
Simple answer? -> yes you can measure the moisture content at which you achieve 20mm penetration with the cone penetrometer which has been taken to correspond to the liquid limit, but the test method may not be sufficiently repeatable for soils which are non-plastic. I guess it all comes down to what you are trying to prove, or more importantly who is trying to use the information.
We used to have to determine the plasticity index of rock armour, the material had no fines (less than 0.0001% of the overall mass), but if you tried hard enough you could get enough to do a test. But was the fact that these were plastic of any relevence when you consider the sample as a whole?