Is it possible to send / retrieve MMS messages via WiFi or is it mandatory to be connected to my provider via the mobile data connection?
If a user has an active WiFi connection, what happens when there's an incoming MMS?
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.
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).
As others have mentioned, the only way to receive a MMS directed toward the number serviced by your carrier is for you to be connected to their service. However, you might consider a service such as Google Voice. Google Voice provides an alternative number that is then routed to your phone. Currently Google Voice only supports SMS, but there may be other services that offer MMS support. A SMS message sent to your Google Voice number would then be visible in the Google Voice app, even if you only have a WiFi connection.
I think that most (smart) phones do not know how to create a separate IP socket to send/receive MMS over wifi. So they revert by default to the data socket provided by the carrier. Or they may not have the ability to switch between two different sockets automatically. If you do root your phone and change the default MMS IP socket, you may lose all MMS connectivity depending on the phone.
This is an old thread, I know, but I wanted to add that the Nokia N900 multimedia messaging app could receive notification of a MMS via the cellular network and retrieve the MMS, itself, via the Internet, at least on Wind (now Freedom Mobile) in Canada. This avoided roaming data charges and is the one feature that I miss most from my N900, now that I am using an Android phone.