Suppose I have this table
parent | child
1 2
1 3
2 4
4 5
5 6
and I want to check if 6 is a descendant of 1 (which it is)....can I accomplish this within one single query, or will I have to inevitably get all data and process them with PHP?
You can walk the tree using recursion in MySQL without processing the data in PHP. MySQL doesn't support true recursion though, so you'd have to settle for some recursive-ish techniques:
One method is described in this SO question, but would involve changing your tables.
Another method would be by using a stored function, which will loop through the table until the job is done (which is recursive in a way). This would probably work with your current table, but is more complex to achieve.
I have an example right here that walks a TYPO3 pages table, finding all page ID's for a given rootline (comparable to what you're trying to achieve):
BEGIN
DECLARE _id INT;
DECLARE _parent INT;
DECLARE _next INT;
DECLARE CONTINUE HANDLER FOR NOT FOUND SET @id = NULL;
SET _parent = @id;
SET _id = -1;
IF @id IS NULL THEN
RETURN NULL;
END IF;
LOOP
SELECT MIN(uid)
INTO @id
FROM pages
WHERE pid = _parent
AND uid > _id
AND deleted = 0
AND hidden =0;
IF @id IS NOT NULL OR _parent = @start_with THEN
SET @level = @level + 1;
RETURN @id;
END IF;
SET @level := @level - 1;
SELECT uid, pid
INTO _id, _parent
FROM pages
WHERE uid = _parent
AND deleted = 0
AND hidden = 0;
END LOOP;
END
Excuse me for not having the time right now to tailor this example to your needs, making this an incomplete answer, but I'm hoping this can get you on the right track nonetheless.