¿Orden de operaciones de MySQL?

Supongo que está interesado en SELECT , según la documentación de MySQL la sintaxis es la siguiente

SELECT
[ALL | DISTINCT | DISTINCTROW ]
  [HIGH_PRIORITY]
  [STRAIGHT_JOIN]
  [SQL_SMALL_RESULT] [SQL_BIG_RESULT] [SQL_BUFFER_RESULT]
  [SQL_CACHE | SQL_NO_CACHE] [SQL_CALC_FOUND_ROWS]
select_expr [, select_expr ...]
[FROM table_references
[WHERE where_condition]
[GROUP BY {col_name | expr | position}
  [ASC | DESC], ... [WITH ROLLUP]]
[HAVING where_condition]
[ORDER BY {col_name | expr | position}
  [ASC | DESC], ...]
[LIMIT {[offset,] row_count | row_count OFFSET offset}]
[PROCEDURE procedure_name(argument_list)]
[INTO OUTFILE 'file_name' export_options
  | INTO DUMPFILE 'file_name'
  | INTO var_name [, var_name]]
[FOR UPDATE | LOCK IN SHARE MODE]]

Sí, puede usar columnas definidas con AS en el GROUP BY cláusula.