@Divya Konasani Thank you for posting your query on Microsoft Q&A and for using Azure services.
My understanding is that you are looking to know according to the above scenario if you application will still traverse central us region even though the preferred location is east us. And what happened if the whole central region is down with private endpoint enable on central us. Please let me know if my understanding is not correct.
The answer to your question is private endpoints are transparent to the application. If you select east us as your preferred locations, then the request will go to east us locations. If the region goes down, failover will happen as expected. Achieve high availability with Cosmos DB
Coming to Azure container register I saw the tags was added below the question. I will check with the team if that is the similar behavior.
Regards,
Oury