Is there a conditional tag to determine whether the post is _any_ custom post type?

I don’t know of a conditional tag, but here’s how you would list the built-in types:

echo implode(',', get_post_types( array('_builtin' => true ) ) );

Output:

post,page,attachment,revision,nav_menu_item

Maybe better:

// 1 result if it exists and is builtin, 0 otherwise
get_post_types( array('_builtin' => true, 'name' => $post_type ) );