no, you would still need the where clause at the end of the SELECT .. FROM ... INNER JOIN... ON.. statement i provided. so the full sql statement would be:
SELECT featured_shows.feature_id, featured_shows.event_id, featured_shows.feat_title, calendar_event.id, calendar_event.date_start
FROM featured_shows
INNER JOIN calendar_event
ON featured_shows.event_id = calendar_event.id
WHERE DATE_FORMAT(calendar_event.date_start, '%Y-%m-%d') >= DATE_FORMAT(now(),'%Y-%m-%d')