[Solved]-Highcharts Pie Chart Label Threshold-Highcharts

a very late answer to this question:

if instead of returning empty string, you instead return null, the label and connector will not show, and you'll be able to achieve this effect without removing the connector:

example: jsfiddle

plotoptions: {
    pie: {
        datalabels: {
            formatter: function(){
                if (this.percentage < some_value) return null;

                return value_to_show;
            }
        }
    }
}

the best way to achieve this is to use datalabels formatter for pie chart like this:

plotoptions: {
    pie: {
        datalabels: {
            formatter: function(){
                if (this.percentage < some_value) return "";

                return value_to_show;
            }
        }
    }
}

replace some_value and value_toshow with desired values. but there will be some problems if you're using connector for you labels (it is always visible).