I had a customer ask if after they were done migrating all their mailboxes and services from their local on-premises Exchange Server to Exchange Online if they could remove their local Exchange server. You certainly cant blame them for wanting to with the recent news of zero-day vulnerabilities for Microsoft Exchange Server that are being actively exploited and that Exchange Online was not at risk.
I remembered a great article posted a few years back by Paul Cunningham on Practical365.com and in it the following:
“If you have directory synchronization in place, then you need to manage the mail attributes of users, groups, and contacts in the on-premises Active Directory, and then allow those changes to synchronize to Azure Active Directory. The only ๐๐๐ฝ๐ฝ๐ผ๐ฟ๐๐ฒ๐ฑ way to manage the mail attributes on-premises is using the Exchange management tools, which requires at least one Exchange server to be running.”
https://bit.ly/38HYltb
The key word is ๐๐๐ฝ๐ฝ๐ผ๐ฟ๐๐ฒ๐ฑ and sadly no new updates from Microsoft have come since 2017 so for now the answer is no you must keep at least one Exchange Server on-premises and this has been your #MicrosoftCloudQuickFix