The desired functionality cannot be implemented with built-in properties. From the code behind the editor is expected to be set with an ordinary string value by design.
You could use a custom implementation, which gets the html file, retrieve its content as text and sets the editor's content with the value of the body elements.
This is an example code, which is working fine on my end:
string mslinepath = Server.MapPath("TemplateFolder/template.html");
string htmlCode = File.ReadAllText(mslinepath);
int startIndex = htmlCode.IndexOf("<
string content = htmlCode.Substring(startIndex, endIndex - startIndex);
RadEditor1.Content = content;
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