I’ll let those who are more familiar with the sartorial scene in Georgia reply to the question you asked immediately above.
In response to the general question that constitutes the topic of this thread, I’d say that the appropriateness of a madras tie depends not on the calendar but on the weather, on the other items you are wearing, and on the setting.
Don’t look at Labor Day as a Berlin Wall but, rather, as a wide, fuzzy border. None but the anal-retentive need be overly concerned about it.