For all others interested:
I've achieved it by modifying introspector class, set_posts_query function, where I've just added this line:
$query['post_status'] = array( 'publish', 'future' );
before last if.
This is quite primitive way and probably will not work well in case of other post_status values (authorization consideration if status is draft) but works fine for planned posts.
I don't know php and maybe that's why I don't understand, how it works, that in the mentioned function there are lines of sort:
some_var = $json_api->query->post_type
i.e. post_type field is referenced, but I couldn't find any definition/declaration of post_type field in query object, which is JSON_API_Query type, as far I understand.