Is there a method or property that indicates (server-side in code behind) whether or not the user has made any changes to the text that was originally loaded into the editor control?

You can do some thing like this:

 

<script runat="server">
 
   string temp;
   void Page_Load(object sender, System.EventArgs e)
   {
      if (!IsPostBack)
      { 
        Editor1.Text={get your data source};        
        temp={get your data source};
      }  
 }

 public void Submit(object sender, System.EventArgs e)
 {
    if(temp==Editor1.Text)
    {
      //not changed
    }
    else
    {
      //changed
    }
 }
</script>

 

Hope it helps. Let me know if you have any further questions.