Hi @rohanrajan_hms
No, annotation layers are not part of network diagram layer. Network diagrams don't support annotation.
First of all, there is no way to query the annotations stored in the annotation class that are related to the only diagram features in the active diagram. Moreover, if you apply a layout to your diagram, the diagram feature geometry changes and the annotations are no longer properly placed.
Nothing prevents you to set up the labels you want on your diagram features using the standard labeling engine or the Maplex labeling engine and make these labeling customizations apply by default for any diagram you will reopen or any new diagram you will create, but these labeling customizations cannot be done through annotations.
Regards,
Anne-Yvonne