Can apex:param pass null for Integers?

It looks like the problem is that when the parameter comes over as an empty string, salesforce converts the value to 0 instead of NULL. You could consider setting the value of index in your method based on the param value string:

public void doSomething() {
    String ParamValue = Apexpages.currentPage().getParameters().get('indexValue');
    index = ParamValue == '' ? NULL : Integer.valueOf(ParamValue);
    System.debug(index);        
}