I may not be the best one to respond to this, since we haven't done a lot with report emailing in Tableau Server. But since this question has gone most of the day without a response....
If you're using Tableau Server's built-in subscription system to send emails, I would guess that your options are almost nil. Tableau Server itself is going to ignore auto-responder emails, so you're not going to get any analytics from it.
One solution I thought of is to construct the emails with a "Reply-to" address that actually goes to a human, so they can collect and compile the auto-responses into the list that you require. To my knowledge, Tableau Server can't be configured with a "Reply-to" address. The solution, then, is to write a script using tabcmd and an email program to send the emails, at which point you have more control.
Here is a thread that discusses using tabcmd in conjunction with febootimail to send emails out.
I'm not real familiar with febootimail, but it does have a -REPLYTO command line option.
I hope this helps!