Outlook Client Experience Following Migration To New O365 Tenant

We are migrating a customer from one O365 to a new tenant, we are also transferring their SMTP domain to the new tenant as well. 

We are using a third party tool to do the heavy lifting and transfer the mailbox data between tenants and the tool includes an agent to be deployed onto the client machines to create a new Outlook profile for the users following the migration. Due to difficulties in getting software deployed in their current estate our customer has asked what the user experience would be like if they didn't use the tool to create new Outlook profiles.

The scenario would be on Friday night a user has a mailbox on TenantA with a primary SMTP address of user@domain.com and Outlook pointing at their mailbox on TenantA. All mailboxes are migrated over the weekend and domain.com is removed from TenantA and added to TenantB and all relevant DNS entries are updated. On Monday morning the user would have a new mailbox on TenantB with a primary SMTP address of user@domain.com, they would also still have a mailbox on TenantA but the only SMTP address it would have would be user@tenanta.onmicroisoft.com. How would Outlook behave if they opened it up without creating a new profile to point to their mailbox on TenantB? Would autodiscover kick in and reconfigure the profile to point to TenantB, would it connect them to the mailbox on TenantA that still exisits (albeit with a different SMTP address) or would it just fail to connect to anything?

Thanks in advance.