The GmailApp service of Google Apps Script doesn’t support drafts creation but you use the Gmail API to programatically create drafts in your mailbox.

You can create basic HTML drafts or you can also create drafts with attachments as shown in the following example. It can also be extended to create duplicate drafts in Gmail - you fetch the source draft using the Gmail API itself, parse the MIME message, edit the text or html if required, and save it as a new draft.

// Written by Amit Agarwal
// Web: ctrlq.org
// Email: amit@labnol.org

function createDraftMessage() {
  var attachments = ['File_ID_1', 'File_ID_2'];

  var message = {
    to: {
      name: 'Google Scripts',
      email: 'amit@labnol.org',
    },
    from: {
      name: 'Amit Agarwal',
      email: 'amit@labnol.org',
    },
    body: {
      text: "Mr hänn is schon lang nümme g'she.",
      html: "Mr hänn is schon **lang nümme** g'she.",
    },
    subject: 'ctrlq, tech à la carte',
    files: getAttachments_(attachments),
  };

  // Compose Gmail message and send immediately
  callGmailAPI_(message);
}

function callGmailAPI_(message) {
  var payload = createMimeMessage_(message);

  var response = UrlFetchApp.fetch('https://www.googleapis.com/upload/gmail/v1/users/me/drafts?uploadType=media', {
    method: 'POST',
    headers: {
      Authorization: 'Bearer ' + ScriptApp.getOAuthToken(),
      'Content-Type': 'message/rfc822',
    },
    muteHttpExceptions: true,
    payload: payload,
  });

  Logger.log(response.getResponseCode());
  Logger.log(response.getContentText());
}

// UTF-8 characters in names and subject
function encode_(subject) {
  var enc_subject = Utilities.base64Encode(subject, Utilities.Charset.UTF_8);
  return '=?utf-8?B?' + enc_subject + '?=';
}

// Insert file attachments from Google Drive
function getAttachments_(ids) {
  var att = [];
  for (var i in ids) {
    var file = DriveApp.getFileById(ids[i]);
    att.push({
      mimeType: file.getMimeType(),
      fileName: file.getName(),
      bytes: Utilities.base64Encode(file.getBlob().getBytes()),
    });
  }
  return att;
}

// Create a MIME message that complies with RFC 2822
function createMimeMessage_(msg) {
  var nl = 'n';
  var boundary = '__ctrlq_dot_org__';

  var mimeBody = [
    'MIME-Version: 1.0',
    'To: ' + encode_(msg.to.name) + '<' + msg.to.email + '>',
    'From: ' + encode_(msg.from.name) + '<' + msg.from.email + '>',
    'Subject: ' + encode_(msg.subject), // takes care of accented characters

    'Content-Type: multipart/alternative; boundary=' + boundary + nl,
    '--' + boundary,

    'Content-Type: text/plain; charset=UTF-8',
    'Content-Transfer-Encoding: base64' + nl,
    Utilities.base64Encode(msg.body.text, Utilities.Charset.UTF_8) + nl,
    '--' + boundary,

    'Content-Type: text/html; charset=UTF-8',
    'Content-Transfer-Encoding: base64' + nl,
    Utilities.base64Encode(msg.body.html, Utilities.Charset.UTF_8) + nl,
  ];

  for (var i = 0; i < msg.files.length; i++) {
    var attachment = [
      '--' + boundary,
      'Content-Type: ' + msg.files[i].mimeType + '; name="' + msg.files[i].fileName + '"',
      'Content-Disposition: attachment; filename="' + msg.files[i].fileName + '"',
      'Content-Transfer-Encoding: base64' + nl,
      msg.files[i].bytes,
    ];

    mimeBody.push(attachment.join(nl));
  }

  mimeBody.push('--' + boundary + '--');

  return mimeBody.join(nl);
}