While we haven’t tested this approach specifically on the product team, one of our newly minted MVPs Anton Gritsenko (aka @FreemanRU), has figured out how to use Office 365 as the outbound notification server from Service Manager. The approach still requires a on-premise SMTP server but you are just using it to relay the emails to the Office 365 server.
You can read about the approach on his blog here:
Keep in mind this is for outbound emails. Inbound email processing using the out of the box workflow with SCSM still requires a folder share where the email files are processed from. Alternatively, you can use the Exchange Connector to process inbound emails. Only the soon to be released Exchange Connector 3.0 is able to process inbound emails coming into a Office 365 Exchange Server in the cloud. Since I get at least 10 people a day asking me about this… The EC 3.0 RC should be coming out early next week.
Very clever Anton! Thanks for sharing with us!