Theoretically. Practically, you're hunting for the reason why your GitHub token doesn't allow you to install a private package from another repository in your org during the build, then you learn you need a classic personal access token tied to an individual user account to interact with GitHub's own package registry, you decide that that sounds brittle and after some pondering, you figure that you can just create a GitHub app that you install in your org and write a small action that uses the GitHub API to create an on-demand token with the correct scopes, and you just need to bundle that so you can use it in your pipeline, but that requires a node_modules folder in your repository, and…
Oh! Could it be that you just added complexity for complexity's sake?