I'm not looking for meshing necessarily. I'm just looking for a way to e.g. create an IoT device that one can connect to directly without that device necessarily being connected to an AP, and the connecting device can maintain connection to the internet through an AP.
My understanding is that WiFi direct was intended (at least partially) as a potential replacement for Bluetooth. For example, you could have a mouse built around an esp8266 and connect it to your laptop via WiFi Direct. You wouldn't want to have to pair it with an AP when you take your laptop somewhere else, but you still want your laptop to be able to connect to an AP.
The FAQ on this page:
http://www.wi-fi.org/discover-wi-fi/wi-fi-direct implies that a device can (optionally) support connection to an AP and other connections via WiFi Direct:
* Can a device simultaneously connect to a regular Wi-Fi network and a group of Wi-Fi Direct-certified devices at the same time?
All devices certified under the Wi-Fi Direct program allow the user to connect to an infrastructure or a Wi-Fi Direct-certified network. Some devices certified under the Wi-Fi Direct program support connections to both an infrastructure network and Wi-Fi Direct-certified group at the same time (e.g. a laptop may support an infrastructure connection while also belonging to a Wi-Fi Direct-certified group). Simultaneous connection to a Wi-Fi Direct-certified group and an infrastructure network is an optional feature.