I just picked up a 3G iPhone yesterday morning, so I'll try to answer your questions/thoughts Wazoo.
The iPhone doesn't come with an email account of its own. As far as the AT&T plans are concerned, you get a certain amount of minutes, "unlimited" internet access, and a text messaging package if you so choose. So there is not an "AT&T Account" that you can forward things to.
The native iPhone push setup is Apple's $100/year
MobileMe package, which is basically an Exchange clone with the addition of disk space and a few other frills. You get a web-based package of email/contacts/calendar on the communications side, and a 20GB iDisk for storing files remotely and sharing them as the case may be. It's fairly swank when it's working right, but I doubt you could convince anyone here that it was worth $100/year.
MobileMe can then push to the iPhone, PC, and Mac. The iPhone/Mac bit is more or less self explanatory since Apple built it in to the OS. For the PC, iTunes comes with a MobileMe sync agent that keeps Outlook 2003/2007's contacts and calendars in sync with the service; email is handled via IMAP. On the whole the service in theory works rather well, but they're still having launch pains at the moment. In either case it works better on the Mac than the PC.
Perhaps the more important bit is that the iPhone also supports Microsoft's Exchange
ActiveSync technology for integrating with Exchange. This includes all of Exchange's push features, and is the intended push method for business users. Ultimately if Spamcop wanted to offer a push service, they'd have to use a package that supported ActiveSync such as
Z-Push.
At any rate, the easiest solution right now would be to forward all Spamcop mail to a MobileMe account, which could then push said email out. Dealing with sent mail would be a bit tricky however; you'd have to set up Spamcop too via IMAP/SMTP and then tell the iPhone to save sent mail in the Sent Mail folder, but I'm not sure how to tell the iPhone's Mail.app to not check the inbox (since we want it all going to MobileMe in this case).
I don't think anyone would complain however if Spamcop did offer Push services, even if it was at an extra fee.
Edit: Apparently the default Yahoo configuration on the iPhone operates in a
Push-IMAP configuration if you use Yahoo's paid email service, so you could also forward your email to Yahoo and have it push out that way. That's certainly cheaper than MobileMe ($20 versus $100) although it lacks the contacts & calendar pushing, and still presents the problem of having yet another intermediary. It does give a bit more of a competitive reason for Spamcop to offer push services however.