The iOS SDK class MFMailComposeViewController can be used to let the user compose an email message.
What I’d like to do, is for the iOS app to send an email in the background, with no user interaction. Is this at all possible/allowed in the iOS SDK?
Nope. There isn’t any API available to do this. You’d need to roll your own SMTP client and have the user enter credentials into your application. On top of that Apple may not approve this.