My question was, will the remove() method from an Iterator over a Set returned by Map.keySet() un-map the item from the underlying Map?

The answer is yes!

The set supports element removal, which removes the corresponding mapping from the map, via the Iterator.remove, Set.remove, removeAll retainAll, and clear operations. It does not support the add or addAll operations.

That is some fine documentation, folks!  As developers on our own systems, we know that our peers can always look at the code and try to figure out what is going on.  But, having documentation that allows the clients of your class to easily answer questions is vastly superior to people regularly resorting to looking at your code.