The Constitution trumps all acts of Congress, including the Patriot Act. A court deciding to enforce an act of Congress does not do so by saying the law trumps the Constitution, it does by saying the law does not violate the Constitution. Big difference.

First off, the Supreme Court is a court of selective jurisdiction, meaning that there are no automatic appeals to it (in most cases, perhaps there are automatic appeals in federal death penalty cases, but I am not sure). The Supreme Court chooses which cases it will hear. A party wanting its case heard by the Supreme Court must file what is known as a writ of certiori, which the Supreme Court may or may not grant (it usually will not opt to review the case).

While I find that hypothesizing how the Supreme Court will decide an issue is usually fruitless, let alone in a hypothetical case, I will say that, in general, time, place and manner restrictions on constitutionally protected activity are generally constitutional. In other words, while a law banning prayer would almost certainly be unconstitutional, a law banning prayer in the middle of an intersection would likely be constitutional. Further, the TSA or FAA directive in question does not likely specify prayer as a prohibited activity. More likely, the act prohibited is standing in that part of the aircraft. A person standing in a prohibited part of the aircraft would be in violation of this rule regardless of his reason for being there. In other words, one cannot trump such a rule by engaging in constitutionally protected activity.

Finally, the aircraft is the private property of American Airlines. The ability of a private entity to regulate activitiy on private property is well established. Even if the policy is designed to comply with a TSA/FAA rule, the fact that it is being enforced by a private entity on private property makes it highly unlikely that anything in the above described situation would implicate the Constitution.