Is using Drupal for a frontend and a non-Drupal API for a backend possible?
Drupal 7/8 can make use of Remote Entities which could be provided in a JSON format. But, what your describing seems needlessly complex. If you have a JSON based backend I would do something more simple like create the frontend using Javascript to talk to your backend, or maybe using a more generic php framework.

Attempting to use Drupal as a frontend and ignoring its data creation CRUD, Content Types and storage mechanisms -- sounds like big headache.