I agree with Miles about the motivation for desertion. If the Galvanized men learned they were being sent to New Orleans they might well have deserted out of self defense. It probably would not have gone well for them if they were recognized in New Orleans wearing a Yankee uniform.

The forced enlistment of foreigners I mentioned took place in the first few months of the war. John D. Winters' book "The Civil War in Louisiana" gives some details and states that a number of Englishmen were released when they complained to the British consulate.