I have been looking into this recently and from my research,(please see "Device to device communication with WiFi Direct: Overview and experimentation" by Daniel Camps-Mur,....) the WiFi Direct does NOT create ad-hoc network. It's actually creating a WiFi infrastructure network where one party takes the role of AP (soft-AP). Once this established, the network works much like a normal WiFi network. Do we agree on this?
Given this is the fact, Apple iPhone should be able to connect to WiFi Direct device that is already set up as AP. I haven't check this though.
Having said this, How can you get an Android phone like Samsung Galaxy S3 or S4 to act as AP? there is nothing in the settings as far as I know. If you connect two such devices, one of them will take the role of AP. Now, iPhone will detect the established network, but when trying to connect to that, will be asked for WPA password. Good luck finding it! Cus you can't get it from the phone. I read somewhere that a file in Samsung Galaxy called WPA_Suppliciant.conf has the WPA key in it but I didn't see it there.
I believe if you could find WPA password, you can get the iPhone to easily connect.