I’m not a Constitutional lawyer or even a scholar, but my layman’s guess is it would not be. The NLRB has no authority to regulate interstate commerce, which in essence is what they are doing. I can find words in the Constitution to the effect that Congress has that authority, but it makes no mention of the National Labor Relations Board. I can find no words in there that even mention it.
So Boeing doesn't need to appeal anything. It can ignore the Board unless and until the Board seeks enforcement of the Order with an appropriate court. That's where the real fight will be.