MySQL:alternativas a las subconsultas anidadas al limitar los datos agregados en una subconsulta correlacionada

No, no puede usar subconsultas correlacionadas en FROM cláusula. Pero puedes usarlos en el ON condiciones:

SELECT AVG(d.DailyData1) Data1_20DayAvg 
       --- other aggregate stuff on d (Datatable)
FROM 
      ( SELECT '2012-01-23' AS DateChecked
      ) AS dd
  JOIN
      DataTable AS d
    ON
      d.Date <= dd.DateChecked
    AND
      d.Date >= COALESCE( 
      ( SELECT DailyData1 
        FROM DataTable AS last20 
        WHERE Date <= dd.DateChecked 
          AND (other conditions for last20)
        ORDER BY Date DESC 
        LIMIT 1 OFFSET 19
      ), '1001-01-01'   )
WHERE (other conditions for d Datatable)

Similar, para muchas fechas:

SELECT dd.DateChecked 
     , AVG(d.DailyData1) Data1_20DayAvg 
       --- other aggregate stuff on d (Datatable)
FROM 
      ( SELECT DISTINCT Date AS DateChecked
        FROM DataTable 
      ) AS dd
  JOIN
      DataTable AS d
    ON
      d.Date <= dd.DateChecked
    AND
      d.Date >= COALESCE( 
      ( SELECT DailyData1 
        FROM DataTable AS last20
        WHERE Date <= dd.DateChecked 
          AND (other conditions for last20)
        ORDER BY Date DESC 
        LIMIT 1 OFFSET 19
      ), '1001-01-01'   )
WHERE (other conditions for d Datatable)
GROUP BY 
      dd.DateChecked 

Ambas consultas asumen que Datatable.Date tiene un UNIQUE restricción.