Please keep them in the carrying case! Don't worry about the pressure and temperature, but if they are banging around in your baggage outside of the case, I can almost guarantee they will be damaged.
Remember, they are made from wood, and not unlike—let's say—a fine musical instrument such as a violin, they are susceptible to impact damage if mishandled.
[fun fact: I modeled the carrying case after violin cases]
As far as NightHawk usage during a flight...I have done so many times. The noise isolation (both ways in and out) with NH is much greater than typical open-back 'phones. In fact, NH noise isolation is on par with or greater than some closed-back headphones. So far I haven't received any complaints from neighbors, but you might pre-warn your row mates to alert you if they can hear your tunes.
The isolation is good enough that you can expect about 15 to 20 dB reduction of cabin noise above 1kHz. If you need LF reduction, then active noise cancelling is the only way.
Regardless, they work surprisingly well during flight. The only detriment is that they are physically large; after all, they were designed more for desktop use.