Being physically connected to the network through ethernet generally will not help you obtain the network's wireless password, unless there is some other kind of vulnerability - for insance, an unprotected router admin page, or perhaps a vulnerable client connected to WiFi that you can break into and extract the password from (fairly unlikely).
Authentication between wireless clients and the access point occurs over the air; this communication does not travel over the wired portion of the network so being connected to ethernet does not give you a significant advantage. Plus, even if you capture the authentication packets you'd still have to perform a brute force attack on the wirelessly-transmitted WPA handshake to obtain the original password, something that can be done without connecting to the network at all.