​​I have created a script that copy template table from one docs to another.

function onOpen() {
  var ui = DocumentApp.getUi();
  ui.createMenu('Templates')
      .addItem('some_items', 'appendTemplate')
      .addToUi();
}

​function appendTemplate() {
    var sourcedoc = DocumentApp.openById("DocID");
    var sourcebody = sourcedoc.getBody();
    var tables = sourcebody.getTables();
    var table = tables[0].copy();
    var destdoc = DocumentApp.getActiveDocument();
    var destbody = destdoc.getBody();
    var x = destbody.appendTable(table)
}

When I exec this script the table correctly copy to target document but dropdown boxes are without default colours.

when I tried to click any of them I got an error "unable to load file".