Is it possible to get the password from a wps wifi connection?
Yes, WPS is insecure and the WPS PIN can be used to recover the password.

This app and this app claim to be able to do so if you have root.

However, as pointed out by Izzy the password should also be available as plain text in the file /system/etc/wifi/wpa_supplicant.conf after you have successfully connected to the network once.