Eric,
Please use the following code instead:
// get the cute editor instance
var editor1 = document.getElementById('<%=Editor1.ClientID%>');
//Get the editor content
var editdoc=editor1.GetDocument();
var head = editdoc.getElementsByTagName("head")[0];
alert("Before:"+head.innerHTML);
var style = editdoc.createElement(SomeStyleSheetPath);
head.appendChild(style);
alert("After:"+head.innerHTML);
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