Hi Bob,
What is your source table in and what is the definition of the List01_Id field? What method are you using in ArcGIS to import it? To what type of geodatabase are you importing it? What version of ArcGIS are you using?
I tried Import > Table (single) and copy/paste from ArcGIS 10.1, with source tables in a SQL Server database that contained a not null, smallint field. My destination geodatabases were an enterprise geodatabase in SQL Server and a file geodatabase. In all cases, a separate ObjectID field was added to the table; it didn't convert my smallint ID field to an ObjectID.
But there are many different source and destination types you could have used, so please respond with the specifics of your case.
-Kim