Only if the torrent is marked public inside the torrent file itself.
The magnet link is derived from a hash of a portion of the torrent file which includes the public flag/setting - which controls whether DHT/similar "trackerless" methods can be used for transmitting.
Without the public flag set, a magnet link for that torret is pretty much useless to a torrent client since it won't be able to discover any other peers.
