Can I use Google's new CardDAV-based contacts sync to sync between my Exchange contacts and Google contacts on my iPhone?

I want my Google contacts and my Exchange contacts to sync through my iPhone as follows: Google contacts iPhone Exchange contacts and I was looking at Google's CardDAV sync as a way to do it. http://gmailblog.blogspot.com/2012/09/a-new-way-to-sync-google-contacts.html?m=1 First, is this even possible? What I can't understand is that after you add the CardDAV account to the iPhone your new contacts must go in that specific contacts group in order to sync. But of course they won't sync to Exchange since the Exchange contacts by definition are in their own group. Can I do this?