Can fetch() do responseType=document?

XHR's responseType='document' is awesome because it hands you back a DOM document that you can use querySelector, etc on:

var xhr = new XMLHttpRequest();
xhr.open('GET', '/', true);
xhr.responseType = 'document';
xhr.onload = function(e) {
  var document = e.target.response;
  var h2headings = document.querySelectorAll('h2');
  // ...
};

Is this possible with the fetch method?