I am far from being a lawyer but I don't think that would disqualify you from receiving your LTC. I am just curious as to what jurisdictions are actually arresting for this? We simply issued citations or warnings to get it removed.
Since this is a class C misdemeanor and would fall under the same category as if you were arrested for any equipment violation (yes they are arrestable offenses) I wouldn't think there would be a need for a disposition, but someone with more legal expertise may disagree.