Well, if Cordan isn't an Imperial world, than non-Imperial citizens would not count towards an Imperial census (though the Baronial households, if they are all Imperials, would).
The UWP for a planet would (or should) be for the entire population. For worlds within the Imperium, they are defacto Imperial citizens - whether they want to claim their citizenship and travel as Imperial citizens or not. Worlds outside of the Imperium may have census done for their own needs, but it's not performed or handled by Imperial agencies. The IISS might do some data gathering to update their databases, but they would not care to try and implement a census count directly unless it could be done by orbit and the world in question is not strong enough to stop them from being within their orbit.
Worlds with low tech may, or may not, conduct their own, though low-tech governments would be very restricted in their reach. Parts of Europe tried to conduct census efforts a thousand years ago (not sure about Romans, though I'm sure they had something similar, if perhaps cruder). Citizens and slaves were counted, though at the time it was mostly for taxation purposes than anything else. England had it's Domesday book so the king could get what was due to him. I don't know as much about more ancient cultures, let alone Eastern history, but I'm sure similar things were done back then as well.
Don't read too much into the books looking for exacting and logical explanations. You will just end up with a headache.