We just recently sync'ed our AD domain with Exchange Online. Our Exchange had been migrated over a year ago and we have no on-premise Exchange any longer. In the portal, I tried to set a primary SMTP address, and received this error:
The operation on mailbox "John Smith" failed because it's out of the current user's write scope. The action 'Set-Mailbox', 'EmailAddresses', can't be performed on the object 'John Smith' because the object is being synchronized from your on-premises organization. This action should be performed on the object in your on-premises organization.
Our DC's Windows Powershell doesn't support that command. I'd have been surprised if it did.
This is probably relevant- we performed the Sync by changing UPN's on user accounts. The sync works like a charm. But we need to be able to manage accounts.