Just tried it. It connects for a few seconds, enough to recieve messages and attachments, then it disconnects and complains about moving too fast.
Tried it with a Starlink Mini, roam subscription, and opt in Priority data turned off.
Had two 100Wh batteries with me to power it, but ended up using the plane's AC adapter since they had one.
Wanted to try it on my next flight with priority data turned on, but ended up not bothering and sleeping instead. I recall Elon tweeting about a video conference being held from his jet to an employee carrying a Starlink on a commercial flight, looking trough the window.
So the technology is there, but they probably block it to protect the netwrork from overload (same reason we put phones in airplane mode), or to charge extra for the service trough priority data or enterprise licenses.