Conditionally aggregate (count) views field
I have a feeling there may be a solution using a separate view with aggregation and then using the Views Field View module to embed the aggregated view as a field.

Another option (which feels like a bit of a cop-out and cheating) would be to create a content type called "articles count". 

Then each time you do a sync with the external publisher you update the "articles count" node title to be "New [count] articles", and set the body to be a list of links to each of the new articles. This is neat as you always have an index to your new articles.

Then simply include this as one of your content types in the original view. To be honest this is probably the easiest way.