Every time I've ever sent a MMS, it's always switched over to Network Data to send/rec, regardless of if I'm on WiFi. That was the same on my Thunderbolt as well. On that phone, if I was on wifi, it would switch over to the 3G network for the duration of the send, then back to wifi.
So, now that people are up in arms about doing it with wifi on the Gnex, I pose a challenge to those who say they've done it on WiFi:
Go into your settings, and disable mobile data. THEN try to send it on WiFi again, and let me know if it works.
I ask because I simply did exactly that. The first send went through (with arrows blinking on both the WiFi and signal bars). I was expecting to see the WiFi drop away and the 3G pop up for it, but it didn't. So then I disabled mobile data completely, and it just sits here doing nothing while trying to send. Sending...Sending...Sending....and doesn't. So then I re-enabled Mobile Data again, hit resend, and 10 seconds later, sent successfully.
This to me says that it is in fact NOT using WiFi to actually send the message. It's still using the cellular data network (as mentioned above), to do that portion. It just isn't showing it in the notification bar that anything has switched from one side to another.
Give it a go, let us know what happens, maybe mine is just a fluke, but it'd be nice to see people's results with that.