what are the implications of setting up a subscriber as a publisher?
This is known as the republishing model.  It is usually used for balancing distribution loads over slow or expensive links although I have seen it used in the scenario you described as well.  The republishing topology you propose is supported which can be found near the bottom of the page Republish Data, Transactional publication -> Transactional subscription/transactional publication -> Transactional subscription.

If I recall correctly, the challenge with this topology occurs if you ever have to reinitialize COPY_DB, you will also have to reinitialize NEW_DB.