That is what I am suggesting. 
I’m not entirely sure which Dockerfile you’re referring to. I assume you’re building a Docker image with your packages inside? Unless you want to put a secret in there, like an SSH key that has access to your repos, I would advise against actually adding the registry inside the Docker. But the pipeline is given a temporary Personal Access Token (PAT), that gives it read access to all your repos inside the project that it is run in. As long as git is configured inside the pipeline YAML script to use the PAT to authenticate when retrieving your packages, then a private registry works. To set it up, you need to put the git config command I suggested above in a script in the YAML file somewhere before you run julia. Otherwise the package manager won’t authenticate properly.