no user has the Exchange online license on O365, so I know we will need to assign that license once the hybrid is in place
Yes, if you assign Exchange online license before migration, it will create duplicate mailbox for each user. You need assign license to them after migration.
And I believe that I can leave my My MX record alone for now and still have mail delivered through the Barracuda.
During migration, you could keep MX record to local Exchange on-premises. It is suggested to point MX to EOP after migration. If there exist third party filter tool between Exchange on-premises and Exchange online, it may cause a mail flow issue.
Here are two articles which may be useful to you:
- How to sync on-premises Active Directory to Azure Active Directory with Azure AD Connect?
- Exchange/Office 365 Hybrid Configuration Wizard – step by step guide
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