Generally, no. However, I don't think this is the best plan anyways. When you push something public, you should assume all things are public. If there's something you don't want accessed by just anyone, then auth is your answer. That also buys you more flexibility for what it's worth. Whatever needs to communicate locally with this API, may not always live on the same server. If you use auth, you can move it anywhere without issue. Otherwise, it's stuck on the same server, whether that ends up making sense in the long run or not.
Your next best alternative is to separate out the functionality, and host internal-only stuff internally. Trying to make one API serve both internal-only and external requests is only adding unnecessary complication.