FYI- being the nerd I am, I decided to address this question.
The Ford Convenience Charge Cord DOES work at 240VAC.
I put together a rather sketchy adapter (NEMA 10-30 old-style dryer plug to 5-20R 3-prong receptacle), ran an extension cord outside (10ga), then the Ford convenience charger and plugged in.
My only metrics are the fuzzy numbers from MyFordMobile, which had it charging from 69% to 100% in about 286 minutes (just under 5 hours). Given that most of the MyFordMobile metrics appear to be assuming a ~29-30kwh battery (discovered this by downloading the data from that one Chrome extension), this means a net battery charge rate of around 1.9kW. Not sure if that's a full 240V @ 12A with overhead (or if the charge rate would have continued climbing had I waited more than 5 minutes), but it's definitely faster than a 120V charge.
Someday I want to get an OBD-II scan tool (or see if my cheap Panlong adapter will work with FORscan, haven't had luck yet) to get more accurate metrics.
Regardless, I can confirm that the Ford Convenience charger EVSE has a green light when you plug it in a 240V circuit, and the other light blinks green during charging. The car definitely appears to "charge" per the fading/blinking light pattern.
Granted, 5 minutes is a start but not total confidence, I would have to let it charge for 5-10 hours before feeling absolutely confident about using this setup.