As I know, to connecting an access point, wpa_applicant have some states:
- wpa_applicant AUTHENTICATING
- wpa_applicant ASSOCIATING
- wpa_applicant ASSOCIATED
After which we obtain an IP address.
What happens if obtaining IP address fails after wpa_applicant is associated? Are you disconnected?
I've been referring to: https://wiki.archlinux.org/index.php/WPA_supplicant
To understand this, you should study the OSI-layer model.
When the Station is connected to an Access Point, a data link via IEEE802.11 WiFi is created, which happens on the OSI Layer 2, the data link layer.
Communication using IP-addresses is happening on OSI Layer 3, the Network layer, using the Internet protocol.
Both are Independent of each other. When you use the Internet protocol on top of WiFi IEEE802.11, you simply have an IP packet as payload for a IEEE802.11 WiFi data frame. However, a WiFi data Frame can contain any kind of payload, not just IP packets.
Therefore the answer to your question is that you are not automatically disconnected if obtaining an IP address fails (I assume you refer to obtaining an IP address from an DHCP Server running on the Network you are connected to).