Android - Can I send / retrieve MMS messages via WiFi?

It could be done technically. AFAIK all communication between MMS enabled components is done via standard TCP/IP. But in a regular provider setup the MMS store and forward server(s) (MMSC) are only reachable via the providers network. That's why you can not send and receive MMS via WiFi.

It's also the reason why you can not make a call and send/receive an MMS simultaneously when you have only 2G (GPRS/EDGE) connectivity.

Normally android will drop the GSM data connection if there is WiFi connectivity and all data will be routed through the WiFi interface, but there is one exception: The MMS traffic will still go through the mobile data connection.

I dont think it's possible, since the data is sent through the cell network and not through a traditional Wi-Fi style Internet connection.

Your network probably uses a separate MMS APN for multimedia messaging, and these are restricted to the operator's own network, so the messages can't be received via WiFi. Also, the messages are directed to your phone number so this could be compared to using SIP/VoIP through your regular phone number.

If there is an active WiFi connection, it is ignored and packet data is used instead (if enabled).