The way EasyBlog email notifications work is that it sends notification emails to subscribers. So the emails would only be sent to users that subscribes, depending on the type of subscription.
To answer your question, it is not possible to target a specific user group to notify for each blog post that is published. It will only target all the subscribers related to that post. Other than that, the site will not notify the rest.
The workflow you described would fall under customization request.
Having said that, if you require us to perform the customization for you, you can always request for a quote from us at https://crm.stackideas.com
and select "Customizations". Our sales person would be glad to send you a quote for the customizations that you have requested.