Actually no - not on a terrestrial service like gogo. A satellite based service would be different.

And yes - it is blocked, and in addition it's normal practice for Aircell (the company that operates the service) to monitor the traffic being sent over the wireless link from each aircraft, and block any "suspicious" traffic in real time. If you were using a VPN then this would probably be very difficult to detect, but it certainly adds a lot of obstacles. In addition you have the human factor of the passengers around you objecting