Currently, it's not possible to register a document generator for a custom document type when writing an App. I would appreciate it if that could be done through the manifest by declaring a custom document type with a POST endpoint, like:
<admin>
<documentType technical_name="my_document_type" url="https://app.server/my-post-endpoint">
<label>My Document Type</label>
<documentType/>
</admin>

The response of the endpoint would be a PDF document.
In addition, (or alternatively) it would be nice if a custom document type could be marked as “cannot be generated” so that the option to generate a document is not offered in the admin UI.
Then the app could either inject its controls to generate the document or generate the document in a web-hook.