The question is whether a conviction obtained would withstand appeal to the Supreme Court.

See Reid v. Covert 345 US 1.

I am not a lawyer or student of the law, so I would welcome them to criticize my work.

Something I wrote a few years ago:

Attempts to apply the Uniform Code of Military Justice to those that aren’t members of the Armed Forces have traditionally failed. In Reid v. Covert, 345 US 1 (1957) the Supreme Court ruled that “courts of law alone are given power to try civilians for their offenses against the United States.” In that case, a civilian dependent was tried in front of a jury of Air Force officers for the murder of her husband, a member of the Air Force, on an Air Force base in England. Article 2 (11) of the UCMJ was invoked when charges were brought. It reads as follows:
The following persons are subject to this code:

(11) Subject to the provisions of any treaty or agreement to which the United States is or may be a party or to any accepted rule of international law, all persons serving with, employed by, or accompanying the armed forces without the continental limits of the United States....
The Court countered with a quotation from Article III Section II of the US Constitution:

The Trial of all Crimes, except in Cases of Impeachment, shall be by Jury; and such Trial shall be held in the State where the said Crimes shall have been committed; but when not committed within any State, the Trial shall be at such Place or Places as the Congress may by Law have directed.
And the Fifth and Sixth Amendments, respectively:

No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger…

In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed…
The Court continued on to use these passages to rule that the military has no right to try a civilian, and that doing so is a violation of the defendants Constitutional rights. Relevant to the discussion is this passage:

There have been a number of decisions in the lower federal courts which have upheld military trial of civilians performing services for the armed forces "in the field" during time of war. To the extent that these cases can be justified, insofar as they involved trial of persons who were not "members" of the armed forces, they must rest on the Government's "war powers." In the face of an actively hostile enemy, military commanders necessarily have broad power over persons on the battlefront.
It is apparent that this interpretation would allow the military to try private security contractors under some conditions, namely, if the country were at war. Whether the current conflict in Iraq meets the definition of a war is something that would have to be determined by a US Court of Appeals, in the event that a contractor is prosecuted under the UCMJ.