The purpose of this lawsuit is to answer that question. Though I have to say that for the past 9 years, the constitution, judiciary, and legislative branches of the U.S. haven't seemed to have much influence on anything that is supposedly "needed to fight terrorism".
That's not true. The lawsuit doesn't challenge the doctrine of administrative searches, and goes as far as to concede that full-body scans are constitutional as a secondary screening measure (for people who set off the metal detector, or who can't go through the detector, or have prosthetics, or are on a watchlist, or become random selectees).
At issue in this lawsuit is the specific question of whether an electronic strip search can qualify as an administrative search, which must balance the public interest against the intrusiveness of the search.
