Do all entities in Chen notation have to be diagrammatically linked?
Yes, Chen though so and explicitly calls for it his 1976, and 2002 papers. From his 1976 paper, The Entity-Relationship Model-Toward a
Unified View of Data.



From his paper, Entity-Relationship Modeling: Historical Events, Future Trends, and Lessons Learned 2002


  ER Model has Explicit Linkage between Entities. As can be seen in Figures 2 and 4, the linkage between
  entities is explicit in the ER model while in the relational model is implicit. In addition, the cardinality
  information is explicit in the ER model, and some of the cardinality information is not captured in the
  relational model. 


Here is Figure 2,



His contemporaries that cite him also seem to be using explicit links  Hartmann, Sven. "Reasoning about participation constraints and Chen's constraints".  Proceedings of the 14th Australasian database conference-Volume 17. Australian Computer Society, Inc., 2003.



Without the links, you have no relationship. It's a dangling entity.