If the settings are wrong, they are wrong independent of cellular data or WiFi is used.
Here it seems to be about inability to receive/send when connected to WLAN.
That looks like packets are routed wrong way.
--edit
Oh, and you do/should NOT need any data enabled (neither cellular nor data) but need at least GPRS (cell data) availability. As the traffic is sent/received via a completely different APN. Which activates (should activate) on its own.
Talking that I mean Symbian/Maemo/MeeGo times. How Sailfish handles I do not know. But I do hope this has not changed!?

@rob_kouw
but then you should be informed via a SMS that there is something to download on a web site? At least it was that way when I dealt with fMMS on N900.
Cannot remember to have used MMS on Sailfish...

Bu what I also remember is that you needed to have sent one MMS from that phone/SIM to activate the receiving.