That all depends on what permission etc you have granted to the current service accounts and also to the machine account. And here I'm more thinking of Windows permissions than permission in SQL Server.
As for the permissions needed to running SQL Server - no worry, SQL Server Configuration Manager will take care of that. But if you have granted access to the machine account on a file share to permit SQL Server to write backups there or read files for BULK INSERT, you will update those permissions to permit the new service accounts.
In short, you need to have your server(s) documented.