Exchange 2007 Decomissioning after cutover migration to office 365

The whole idea behind a cutover migration is to ditch your on-premises infrastructure, this assumes not just removing Exchange, but generally managing the users directly in the cloud. Thus, no sync. If you plan to use directory synchronization in any shape or form, you need to keep at least one Exchange box on-premises for management purposes, that's the only *supported* scenario. If you don't care about being in a supported configuration, you can remove the last Exchange server and still mange the object just fine via the AD tools.