I am writing a simple game that animates a ball image quickly across a background image.
Would Core Animation/Quartz be sufficient for this scenario?
I don\'
If your knowledge of Core Animation is good then i recommend you to skip learning OpenGL ES for now, since it won't really help you (if all you want is what you described of course). On the other hand, if you plan to make more games which have more involved graphics, it might be a better idea to start learning the API. OpenGL ES is a simple API and you can use the full graphics features of the iPhone with it.
If all you want to do is just make this game, then i say go with what you know and are productive.