This customization would be nice. Is this possible out of the box, and if not, could a developer modify the start screen to make it possible?
Someone also mentioned
The Time by Jeff Key. Here is a page that talks about it.
Clock Tile is a Windows Store app which lets you see the time on the start screen in Windows 8 using the live tile feature:
There is an app called The Time by Jeff Key in the app store.
Have a look at the top left tile. You can switch between the small and large tile view.