It was not a count of the population because, except with a few exceptions, it did not include members of the armed forces
Members of the Armed forces were in fact 'enumerated' but in a separate Register held by the MOD.
"There are two supplemental paper registers which are not available to the public. One covers those on duty in the armed forces, for example soldiers at an army barracks. The other covers those born after 29th September 1939 and before the paper register ended in 1951."
https://www.whitehousefhc.org/1939%20REGISTER%20160402.docThe National Archives say "Registration of members of the armed forces was dealt with by the military authorities, so the 1939 Register does not include service personnel in military, naval and air force establishments."
So if applying the criteria of "The census is a head count of everyone in the country on a given day." it may well tick that box, although we cannot see those names. Many by 29 Sep 1939 were already abroad serving but only the 1911 and 1921 had enumerated those serving overseas in the Army. When you think about it as it served as the basis of the 1948 National Health Service (NHS) Register all those men + nurses etc had to have then or be allocated later a code number too.
https://www.nationalarchives.gov.uk/help-with-your-research/research-guides/census-records/