No, it is not recommended to use ObjectIDs when joining a table in ArcMap. ObjectIDs are constant as long as the fields are in the original state in the feature class. When records are imported to another feature class or table, new ObjectID values are assigned. The new values causes any relationships based on the original ObjectID values to be lost.
If the relationship is based on another primary key, the ID values are maintained when records are imported. This allows users to maintain relations when related sets of objects are imported to new classes.
Therefore, create a set of fixed field values or user-generated primary keys to join a table.