In order to desert, you must be in service first.
Louisiana state law allowed militia commands to be called into service for a maximum term of 90 days. To the best of my knowledge, Governor Moore never called the Louisiana Native Guards into service. Volunteer militia units which were called into service included the two brigades assigned to defense of New Orleans plus the Cresent Regiment, the Orleans Guards Battalion and the 5th Company, Washington Artillery. The last three were sent to Corinth MS to join Johnston's Army of the Mississippi. When the new state militia law took effect on Feb 15, 1862, the Native Guards went out of existence, so they couldn't be called into service.
Up until Feb 15, 1862, the LNG participated in standard militia assemblies as required under the current law. Standard assemblies included regularly scheduled drills and parades. One company of the LNG may or may not have been present when Federal prisoners-of-war were escorted from the rail depot to prison. None of these activities required officers and men to be away from their homes, each member being able to return to their families by dark and sleep in their own beds.
Following the fall of New Orleans, volunteer militiamen in the city (except for foreign nationals) were ordered to report at Camp Moore. Most of them failed to do so. Again, we can't fault the LNG for not reporting at Camp Moore because they were no longer subject to state militia law.