Jack Balkin says no:
First, the MCA puts the President in an interesting position: the U.S. is still bound by Geneva, but there is no way for individuals to enforce violations of Geneva (except that grave breaches of Common Article 3 can still be prosecuted under the War Crimes Statute). However, Geneva’s status as the law of the land (under Article VI) was not altered by the MCA. The United States has not withdrawn from the Geneva Conventions, and this fact was quite important to selling the bill to the public. So if the President orders procedures that are inconsistent with Geneva, he is still acting contrary to law even though there may be no way for an individual to enforce the law directly.
But that last part seems to be the key: this law forbids anyone from taking a violation of the Geneva Conventions to court. Here is the text of Sec. 7(a):
(a) In General- No person may invoke the Geneva Conventions, or any protocols thereto, in any habeas or civil action or proceeding to which the United States, or a current or former officer, employee, member of the Armed Forces, or other agent of the United States, is a party, as a source of rights in any court of the United States or its States or territories.
So here’s the question: if the legislature and the executive branch both claim the authority to violate this treaty, and the courts cannot hear any case that challenges those actions, how exactly is this treaty still the law of the land? Remember, under our constitution treaties are considered binding law. Once the Senate ratifies a treaty, it is just as legally binding as any other law. But if our government violates it and there is no recourse to challenge such violations, is this not a de facto withdrawal from the treaty?