What kind of migration are you going to perform? AAD Connect is a requirement for most migration types, but if you are planning to do Cutover migration, it's actually required to not have it enabled, as the migration process uses a different method to provision user objects. So in that case you will run it after the migration is complete.
The password sync process does not care whether the user has a mailbox or not. Once you enable PHS, every user in the scope of the sync process will be able to use his AD credentials to access Office 365.