So let's say I get a new iOS device. What happens when I configure it with my existing iTunes account? Will is start populating the home screen with all my paid apps?
I am not really sure what you are asking or how it relates to Mobile Me.
If you set up iTunes to sync across multiple computers then all of your apps/music/movies will transfer automatically.
If you buy a new iOS device such as a new iPod touch and sync it with an itunes account on a computer that you use for another device (say an iPhone 4) then all of your apps paid or free will be available to sync to both devices without any work necessary.
Mobile Me does not play into either of these scenarios though.
GL