No, ObjectID values are not repeated for features in a feature class or for records in a table. The ObjectID field is maintained by ArcGIS and guarantees a unique ID for each row in a table.
An ObjectID is a unique integer field used to identify rows in tables in a geodatabase. Feature classes and tables created through ArcGIS, or created outside ArcGIS and registered with the geodatabase, automatically have an ObjectID field added to the feature classes or tables. The values in this field are maintained by ArcGIS, and the ObjectID is used by ArcGIS to scroll, display selection sets, perform identify operations on features, and so forth.
Therefore, every time a table is created, each row or record added is assigned a unique ObjectID. If a feature or record is deleted, the ObjectID values are not repeated for new features or records in the table.
When working with databases outside of ArcGIS, ensure ObjectID values are not duplicated.