I have just been over this same issue, although my game features a small number of Networked Entities which all need to know about each other constantly ( It is a FPS Based Arena Game ).
As I don't have to deal with Area based Syncing it becomes much simpler but this is essentially the way I do it.
I have a Component on the server version of the Entity that essentially sends out a Sync Update Packet after a specified elapsed time, which is currently about half a second.
On the Client the Packet is Received and stuffed into an Entity Update Message that is sent via the Entity Messaging System to the Entity with the Unique ID and there is another component that basically waits for the Entity Update Messages and then applies them to the Entities Data, whether that is by interpolating the movement or just setting some flags i.e. Casting a Spell.
This is a pretty simple method and seems to work for me, although this one component does need to know about a lot of the Entities Data.
An alternative method would be to create a component that does the same thing but for each set of Data for the Entity.
So If you have Damage Data and Position Data, you could create a PositionSyncUpdate Component and a DamageDataSyncUpdate Component. This is much more fitting but involves creating a lot of Components. This method would be better if your Entities change their Components a lot and is much more reusable. I may potentially change to this method at some point.
Oh as a note, in my system a Component is a class that defines one set of functionality on sets of Data.
Hope this helps somewhat and I haven't completely missed the point
But how does the component access the networking part of the application? How does the server component access NetworkServer?
How do you handle it on the client end? Do you read the package and then send it directly to the component on the given entity?