This is not possible directly, because chronologically, WHERE happens before SELECT, which always is the last step in the execution chain.
You can do a sub-select and filter on it:
SELECT * FROM
(
SELECT A.identifier
, A.name
, TO_NUMBER(DECODE( A.month_no
, 1, 200803
, 2, 200804
, 3, 200805
, 4, 200806
, 5, 200807
, 6, 200808
, 7, 200809
, 8, 200810
, 9, 200811
, 10, 200812
, 11, 200701
, 12, 200702
, NULL)) as MONTH_NO
, TO_NUMBER(TO_CHAR(B.last_update_date, 'YYYYMM')) as UPD_DATE
FROM table_a A
, table_b B
WHERE A.identifier = B.identifier
) AS inner_table
WHERE
MONTH_NO > UPD_DATE
Interesting bit of info moved up from the comments:
There should be no performance hit.
Oracle does not need to materialize
inner queries before applying outer
conditions — Oracle will consider
transforming this query internally and
push the predicate down into the inner
query and will do so if it is cost
effective. – Justin Cave