The simple answer is: no!
While transferring your playlists, Soundiiz only does a matching process from your source service with the destination catalog. That means we are trying to "recreate" a new playlist on the destination service that corresponds to your source playlist as much as possible. Once that is done, we are not deleting your playlist source, and there's no relation between the playlist source and the new one created on the destination.
That is true for "Playlists" and your favorite lists of Artists, Albums, and Tracks. We are only adding them as much as possible with a matching process to the destination and not deleting anything in your source service.
However, be aware that you can manually delete your playlists on Soundiiz. Even if there's a confirmation message to accept before doing such an operation, you must carefully use the "Delete playlist" feature when manipulating Soundiiz.