Can SMS trigger an application?

No - Apple do not allow this type of access. It's almost like saying, why can't I use JavaScript to write files to the users machine and launch applications - it's just asking for security/virus trouble. AFAIK, it's impossible.

2.1 brings apples data push to send stuff to your app. I am not sure if it allows launching of the app or just cacheing of data for the app to access (if its closed).

This is your best bet however, not sms. I assume the running apps can access an sms in the database though?

Good point - I think the push stuff has to go through Apple's servers, as they will maintain the push link to the phone (just a regular poll from the device??).

From a presentation Apple gave I think the user can see little notifications on the app icon, much like when you get new mail or have updates available for your apps. Not entirely sure if they'd expand to launching an app, I'm guessing it's not gonna happen.

I would have thought letting apps access SMS data would be a big security no-no. Even if the app has to ask permission, I can't see it happening.

I'd read it as follows:

1) Your app will not start due to push messages

2) Your app can receive push messages, which will queue until you launch and action those messages

That makes sense. Nothing just opens when an alert is received... except the phone.