Yes, you can use a laptop on planes, after they say its okay after takeoff and before final approach. However, I am told the circuit for the planes is only rated for 75 watts and its not on all seats or airlines. I think it may be restricted to first class or something. I've not been able to find it anyway.
I am not sure what would happen if you plugged it in and started sucking juice. I guess the breaker could flip and shut you down. I am not sure what effect, if any, low power has on either of the adaptors. I suppose it could damage them.
Here's an article on the subject: http://www.strom.com/awards/246.html
In short, I wouldn't count on it. If you need power, you best BYOP!!!