BTW: I know this thread is old, but this is how I ended up doing this just in case anyone else find this useful. zmObject below is what is passed from the doDrop() method. It returns the first message in a conversation when it is a conversation that is dropped.
if (zmObject.TYPE == "ZmConv")
var convListController = AjxDispatcher.run("GetConvListController");
var convList = convListController.getList();
var conv = convList.getById(zmObject.id);
var message_id = conv.msgIds;
var message_id = zmObject.id;