"Note, that even on UNA you only get a server and the site installation. We are not a mail-sending service"

What does this mean?  I would assume at the prices I am seeing for Boonex hosting it will come with PostFix and Dovecot installed.  Does UNA not send out emails in batches like Dolphin did?

UNA does send out emails same as Dolphin. As Baloo correctly noted - apart from sending emails you need a service that maintains high deliverability. It’s a pricey service to provision and it always depends on volume. For example Mandrill will charge $20 for 25,000 emails block. Amazon is cheaper, etc. 

I believe it would be the same for dedicated servers that you provide? If someone gets a $100 server from you and starts sending tens of thousands of emails expecting them all go into main inboxes, then youd have to send them to Mandrill/Sendgid/Amazon, right?