Full Use Case:
I would like to configure automation through Process Builder though if I select to send an email in the document action, it does not fire. How can I get this to work?

Process Builder automation will not work if the Document Action is configured to send an email. If you need to send the document via email, Batch Mode needs to be enabled: In the Process Builder instead of call the Apex Class to “Generate Document,” you need to “Create a Record” on Document Request object, which then will be processed by the RS Documents Batch Mode. If Batch Mode is used, then Process Builder should create new Document Request record. See example screenshot of how Process Builder should look: