Bill,
If you set Editor.EditCompleteDocument Property to true, the editor will process content outside the page body and preserve header tags (e.g. <head>...</head>, <title>...</title>, etc.).
All the elements inside head tag are in your control, include base element.
For example, you can try the following code:
<html>
<head>
<title>Example of the BASE Tag</title>
<base href=http://www.CuteSoft.net />
</head>
<body>
<img alt="" src="http://cutesoft.net/uploads/21.jpg" border="0" />
</body>
</html>
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