The documentation says:
2. The table named on the left-hand side of the AS keyword must appear exactly once in the FROM clause of the right-most SELECT statement of the compound select, and nowhere else.
So your second query is not legal.
However, the CTE behaves like a normal table/view, so you can just join it to the related table:
WITH RECURSIVE q(Id) AS
( ... )
SELECT q.Id, c.Data
FROM q JOIN Component AS c ON q.Id = c.Id
If you want to reuse the computed values in q
for multiple queries, there's nothing you can do with CTEs, but you can store them in a temporary table:
CREATE TEMPORARY TABLE q_123 AS
WITH RECURSIVE q(Id) AS
( ... )
SELECT Id FROM q;
SELECT * FROM q_123 JOIN Component ...;
SELECT * FROM q_123 JOIN Whatever ...;
DROP TABLE q_123;