When the standard iPhone UI controls become too bland, and you want your simple score keeping app to pop a little more with colour, animation, non-standard GUI fonts, and background wallpaper, etc., would it make sense to integrate a game engine for such things?
I've tinkered with Unity3D and Torque2D, and wonder if anyone has used them to make 'normal' (non-game) apps with them vs the default obj-C SDK controls and dialogs?
Can you share your experience please?
This is a very subjective question.
In MY OPINION don't bother - all that hassle for something that you can achieve with a bit of Core Animation and imagination (maybe a bit of creative Photoshopping).
Have a look at Core Animation - theres some very good resources out there that can help you, and you can get designs that "pop" and are interactive without having to resort to using game engines.
If the behavior of your controls is the same as the built-in and just the actual pixels are different, there are some things you can do to skin components.
Buttons are totally customizable with an image. Use stretchableImageWithLeftCapWidth:topCapHeight: in UIImage to stretch the middle and leave the border of the button intact
UITableCellView is meant to be subclassed -- tables are pretty customizable
For a lot of controls, you can turn off some of the look, and then put an image behind them. They still have the behavior of the image.
Use CoreAnimation to add little touches.