Guestimating around 100K+ per month initially. Google Apps Premier allows 2000 per day per user. Which isn't bad for $50/year. That is not a bad option but quite manual.
You just need to set up the Google Apps service manually; everything else (including creating accounts, new addresses, sending emails, creating email aliases, etc.) is fully "automatable" via their API; with wrappers available in Python, PHP, C++, Java, Ruby, Perl, and more....
Authsmtp seems pricey in comparison.