I don't think this would work in practice. My employer sends daily deal emails without using a third-party service like SendGrid or SES and what we do is pay a company like Validity who interface with the big email providers for us. They have honeypot emails that get and validate our emails, they get feedback from the providers on how much they like/dislike us, and we get reports on this.

So an attack like this would be very obvious very quickly, even leaving aside that we'd notice a huge spike in email sign-ups and probably kill their accounts (especially since they're not going to be buying anything from those sock puppet accounts!).