Mine does not have factory NAV. I don't know how the DICE unit works with it so I'd quiz others or call DICE.
The Parrot shouldn't present a problem. I don't know if you want to integrate through the NAV (i.e through stock speakers and have it mute when calls come in) but you don't have to. That adds some complication. The Parrot supports a separate external speaker which is the way I have mine hooked up. Parrot makes one that is small and fits where you need it to.