PSK is technically a L2 authentication, even though there is not actually any "authentication" occurring in the sense of authenticating an identity. In this type of scenario, I sometimes will refer to it as a L2 access, although it is still technically a L2 authentication. If the PSK is valid, then you can transmit frames that the AP can understand, and you will then have access, and can then obtain an IP address. If the PSK is not valid, then the AP will not understand your frames, and you will not be able to get an IP address.
Even an Open SSID technically uses L2 authentication. If you know the SSID, and connect to it, you can then get an IP address. If you don't know the SSID, or don't try to connect to it, you cannot obtain an IP address.
I hope this helps,