@Dasilvak , thank you very much for sharing this detailed analysis and findings. Your analysis is correct for the mentioned scenarios.
Regarding the issue where you were unable to get "Azure Update Management" to work with Azure VM running Linux, can you please check the troubleshooting guide in the following link and see if that helps:
Troubleshoot issues with update management center (preview) for Azure VM running Linux
In case the logs are not helpful, please share the snippet of log message containing the context, to help us get additional details of the issue.
Please let me know if you have any questions.