Is it possible to keep all the DSC configurations in Version Control and make Azure Automation fetch it from there automatically?
The article "Continuous Deployment to Azure Automation DSC", or series of articles, walks through setting up a CI/CD pipeline for DSC using VSTS (Visual Studio Team Services).  Building a VSTS account in Azure is free and it provides some number of build minutes for free as well.

Basically, rather than setting up a runbook, you can configure a CI/CD pipeline using build services in VSTS to perform whatever orchestration activities you require for DSC and VSTS enables you to save your code in their source control management system.