To clarify... you're not moving your on premises users to Office 365, you're syncing them to Office 365.
Will they match? Probably, but you need to understand how hard matching and soft matching works.
Will they have access to their emails with their on-...
I had this issue as well until I discovered the TLS settings between the two systems were in conflict. The server hosting the metadata was set to use only TLS 1.2 while the ADFS server running on Windows Server 2016 was set to the default TLS settings. When I changed the ADFS server to only use TLS 1.2, the issue was resolved.