No, because that'll select any post that contains any of those three tags, not the posts that contain all three tags. AND vs OR.

It's worth noting that I threw the SQL query a bone by denormalizing post_tags into one table. In a properly relational DB, you'd have a tags table, a posts table, and a post_tags join table, so the query gets even hairier (or you have to do two queries).

    SELECT posts.* FROM posts
      INNER JOIN post_tags pt1 ON pt1.post_id = posts.id
      INNER JOIN tags t1 ON t1.tag = "foo" and pt1.tag_id = t1.id
      INNER JOIN post_tags pt2 ON pt2.post_id = posts.id
      INNER JOIN tags t2 ON t3.tag = "bar" and pt2.tag_id = t2.id
      INNER JOIN post_tags pt3 ON pt3.post_id = posts.id
      INNER JOIN tags t3 ON t3.tag = "baz" and pt3.tag_id = t3.id
      WHERE posts.author = "Joe" or post.author = "Jane"
      ORDER BY post_date DESC;

Yikes.

It's also worth noting that this generates a massive temp table to be sorted, which is very likely going to end up causing you to have to do a filesort. In practice, you'd probably break this down into 3 queries (forgive my mixing languages):

    $tag_ids = SELECT id FROM tags WHERE tag IN ("foo", "bar", "baz")

    $post_ids = SELECT posts.id FROM posts
      INNER JOIN post_tags pt1 ON pt1.post_id = posts.id and pt1.tag_id = $tag_ids[0]
      INNER JOIN post_tags pt2 ON pt2.post_id = posts.id and pt2.tag_id = $tag_ids[1]
      INNER JOIN post_tags pt3 ON pt3.post_id = posts.id and pt3.tag_id = $tag_ids[2]
      WHERE posts.author = "Joe" or posts.author = "Jane"

    $posts = SELECT posts.* FROM posts WHERE id IN ($post_ids) ORDER BY post_date DESC;

Easily doable in both languages, but Mongo's denormalized structure makes this sort of use case a ton simpler.