ZENFORMS, yes, I've seen it done that way before. I have a security system at home and the app will inform you of an update when you open it...then you can click to update.
So, the App Store will light up a number on the App Store icon indicating to the user that an update is available. Just wondering why I haven't seen it on my phone? Could be because I used it for development? This is why I purchased the app; so I could experience the entire process from end to end.
Editing my post: The old version of my game on my phone was most likely from Xcode. I went into iTunes and noticed the the game wasn't "installed." So I reinstalled it and now the old purchased version is on my phone. Let's see how it goes.....
One more edit: That was the problem. Once I put the official purchased app back on the phone I received the update notification in about an hour.