You can always do a search in the repository like this: 

{[]:[Field Name]="*"}

That will return any entries with a value in that field.

But I can understand wanting to do a query instead.  You don't have to wait for the program to load a list of entries, and you don't have to work down the list of individual fields.

Here's a query, that when run against your Repository database, checks against the propdef table and the propval table to try to get a count of how many entries have a value in each field: 

SELECT
  def.[prop_id],
  def.[prop_name],
  SUM(
    CASE
      WHEN val.str_val IS NULL THEN 0
      WHEN val.str_val = '' THEN 0
      ELSE 1
    END
    +
    CASE
      WHEN val.num_val IS NULL THEN 0
      ELSE 1
    END
    +
    CASE
      WHEN val.date_val IS NULL THEN 0
      ELSE 1
    END
    +
    CASE
      WHEN val.bin_val IS NULL THEN 0
      ELSE 1
    END
  ) AS value_count
FROM [propval] AS val
LEFT JOIN [propdef] AS def ON def.[prop_id] = val.[prop_id]
GROUP BY def.[prop_id], def.[prop_name]
ORDER BY def.[prop_id], def.[prop_name]

Note that against a test environment with only a few thousand entries, that query wasn't too bad, only taking about 20 seconds to run.  But against a live environment with many millions of entries, it was looking to take MUCH longer to run.  So I added a WHERE statement to limit how many different fields it looks at with each run.  I limited it to 10 fields in this case, and it still took about a minute to run.  Then the next search just requires incrementing the WHERE statement from "1 AND 10" to "11 AND 20", then "21 AND 30", etc., etc. 

SELECT
  def.[prop_id],
  def.[prop_name],
  SUM(
    CASE
      WHEN val.str_val IS NULL THEN 0
      WHEN val.str_val = '' THEN 0
      ELSE 1
    END
    +
    CASE
      WHEN val.num_val IS NULL THEN 0
      ELSE 1
    END
    +
    CASE
      WHEN val.date_val IS NULL THEN 0
      ELSE 1
    END
    +
    CASE
      WHEN val.bin_val IS NULL THEN 0
      ELSE 1
    END
  ) AS value_count
FROM [propval] AS val
LEFT JOIN [propdef] AS def ON def.[prop_id] = val.[prop_id]
WHERE val.[prop_id] BETWEEN 1 AND 10
GROUP BY def.[prop_id], def.[prop_name]
ORDER BY def.[prop_id], def.[prop_name]

EDIT TO ADD: Here's a better query, based on feedback from @████████and more testing of my own.  This was drastically faster to run: 

SELECT
  def.[prop_id],
  def.[prop_name],
  CASE
    WHEN subquery.value_count IS NULL THEN 0
    ELSE subquery.value_count
  END AS value_count
FROM [propdef] AS def
LEFT JOIN (
  SELECT
    def.[prop_id],
    def.[prop_name],
    COUNT(def.[prop_id]) AS value_count
  FROM [propval] AS val
  LEFT JOIN [propdef] AS def ON def.[prop_id] = val.[prop_id]
  WHERE (val.str_val IS NOT NULL AND val.str_val <> '')
    OR val.num_val IS NOT NULL 
    OR val.date_val IS NOT NULL 
    OR val.bin_val IS NOT NULL 
  GROUP BY def.[prop_id], def.[prop_name]
) AS subquery ON subquery.[prop_id] = def.[prop_id]
ORDER BY def.[prop_id]