If you are looking to autopopulate a field based on the value of OBJECTID, your best bet is to create a Trigger in my opinion. When a new record is added and the OBJECTID value is autogenerated by ArcSDE, your trigger will be able to use that value to determine the value of your custom field. However, the trigger will need to fire after the OBJECTID trigger from ArcSDE fires. There is some great online help available for creating basic triggers like this for both Oracle and SQL Server depending on which RDBMS you are using. If you are not using an RDBMS, your options are much more limited and you'll need to take a different approach... most likely using a Python script which is run on a periodic basis.