I think I misunderstood your request. "Template:Short description" is used inside articles, but "Template:Auto short description" is only for documentation purposes. So you actually want articles with a template documented as "short description inducing" without "Template:Short description", right?
I made this query (hope it's correct):
SELECT page_title, LENGTH(pp_value) AS len, pp_value
FROM page_props
JOIN page ON page_id = pp_page
LEFT JOIN templatelinks ON tl_from = page_id AND tl_target_id = 137 # Short_description
WHERE pp_propname = 'wikibase-shortdesc'
AND tl_target_id IS NULL
AND page_namespace = 0
AND page_is_redirect = 0
AND EXISTS (
SELECT 1 FROM templatelinks
JOIN linktarget ON lt_id = tl_target_id
JOIN page ON page_namespace = lt_namespace AND page_title = lt_title
JOIN categorylinks ON cl_from = page_id
WHERE tl_from = page_id AND cl_to = 'Templates_that_generate_short_descriptions'
);
It took 10 minutes and the only returned entry was for en:Main_Page.