of course it will (or at least it's inconceivable to me that it won't).
there are so many questions about this on the web concerning amazon's competing streaming service and i've yet to see anyone mention that amazon serves all the netflix movies from its cloud servers (called AWS, or amazon web services).
every time you stream a netflix movie, no matter to what device, you drop a couple pennies in amazon's bucket.
so they make money either way.