Hello @Cochise-Cloud ,
Thank you for reaching out to the Microsoft Q&A platform. Happy to answer your question.
Any communication from azure VM for Office 365 for email and OneDrive uploads and downloads will be over public internet. It will not be through azure backbone network.
Office 365 for email and OneDrive are not azure services, here is the list of Azure Services https://azure.microsoft.com/en-in/services/.
If the destination address is for one of Azure's services, Azure routes the traffic directly to the service over Azure's backbone network, rather than routing the traffic to the Internet stands correct for those services listed in the above link.
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