No matter how many push apps you will have active, they won't draw any more battery power than one single push app. So if you are using push EMail now, adding any number of push apps won't affect battery at all. That's the beauty of it!
The thing is, all push apps will go through a single central connection. In a traditional system, each push app would have its own connection, and that takes resources. The new system will allow pushing without having the apps needing to run in the background. It's a good solution.
There is one drawback. When a push comes in, it can only do three things, but not the big thing. It can change the number on the icon badge, it can make a sound, and it can show an alert. But it can't actually launch the app and have it do something. The best you can do is show an alert, and a button on it will let the user launch the app - just like when you receive an SMS. Or it can just change the badge, like when you receive an EMail. When you think about it, this is a very small drawback indeed.