Andrew N,
Yes, it does work for Federated domains. I just tested against an identical setup which matches with the setup details that you have provided, the App is working to connect to the mailbox hosted in Office 365/Exchange Online (Cloud). For my setup, I don't have the autodiscover records published for my federated domain/tenant, so if I try to configure my account in the App, which uses autodiscover to pull up my mailbox info, it fails to connect with the usual error. So I then use the Advanced Settings option (provided in the same error message) to setup my account in the App. I provided full SMTP e-mail address (user@contoso.com) in the User name field, outlook.office365.com as Server name, left the Domain field empty & checked the SSL box - it connected right away! I can then use the App as expected connected to that mailbox.