Forum Discussion
What is required to decommission the last on-prem Exchange server?
Follow the official guidance here: https://technet.microsoft.com/en-us/library/dn931280(v=exchg.150).aspx?f=255&MSPPError=-2147217396
Pay special attention to the discussion around DirSync - if you decide to keep DirSync, you have to keep the Exchange box for management purposes if you want to stay in supported configuration.
As to what to do with the remaining mailboxes, it's up to you. Just don't "store" them as PSTs... :)
wroot it's not about what's "possible", but what's "supported". If you know what you are doing, you will be perfectly fine with managing things via ADUC/PowerShell or even the old school command-line tools, but if you run into any issues, Microsoft will simply deny you support. I know a lot of organizations that never had Exchange (moved from Lotus Notes for example), and they often choose to simply extend the AD schema with the Exchange attributes and continue managing the objects using the AD tools. Again, it's perfectly doable, but not a "supported configuration", so you are on your own if something happens.
Btw, recently i had a support ticket because of a mysterious smtp address in our contacts which was tied to some missing mailbox. Support helped with this without i think even asking whether we have on prem Exchange. I don't remember them asking about it at all. Well, maybe our tickets so far didn't require it.