go down in history is an idiomatic expression, so any clause can be used after it. I found some examples of using it with the "as-clause" in the BNC (British National Corpus), so, it is correct and completely acceptable:
Or shall I go down in history as the High Queen who lost Tara for
She could go down in history as the leader who pulled us back from the
Actually, I found out that it is more often to use the expression with "as-clause" than without it, since *go down in history as" is very often used to say how that person went down in history.
The examples of the usage without "as-clause" are the following:
It was a name that would go down in history.
She has gone down in history with this quote when she spotted.