The document also answers some of my questions. Some confusion from the fact that they are using multiple methods in parallel. The scoring networks are resnets. The database was used in training one of the networks.
The generative network section is still unclear, but it looks like it was used in one of their methods, fragment assembly step and network architecture is DRAW (trained with DB). Network generated Fragments inserted using simulated annealing, ranked by either just their conv-net or both existing methods and conv-net. Simulated Annealing hyperparameters were optimized with evolutionary search.
Their third approach is what is most similar to what you describe. It looks like they combine lots of approaches, including features, convnet scores and predictions from other methods. Still needs a lot of detail to be filled in such as more detail on how they integrate memory and how gradient descent is actually done directly on protein chain structures.
It's possible their computational advantage made a large difference in being able to arrive at this result; existing researchers need not feel too bad.