I've always thought that it worked like this: Say, for instance, you're running an IM app with push notifications. You send someone a message, and close down the application. At this point, the application is completely closed on your phone. However, most IM apps keep you signed on for a designated amount of time after you close your connection with their IM server. Now someone responds to your message, and the IM server tells Apple's Push Notification server that you've gotten a message. The Apple server takes the data, and pushes it (like Push email) to your phone. The only battery usage that incurs is the iPhone receives data and displays some sort of alert and maybe a badge for the application icon.
I could be off by a bit, if someone else wants to step in. Apple created the Push Notification system exclusively to help save the battery life of your iPhone, so I doubt they'd allow it to be a huge battery drain (regardless of how many notifications you get). It will use more power, though, but no more then getting an SMS or Email.