If you want to run some script before or after client validation has been performed, you'll need to redirect the WebForm_OnSubmit() function.  Because of the framework we are using, WebForm_OnSubmit() was returning false immediately, so adding anything to Page.ClientScript.RegisterOnSubmitStatement was never being run.

I didn't have time to sort out where in the framework this was being set up (never mind the impact analysis), so I re-directed the Submit of the form to call my function first, then called the WebForm_OnSubmit code as normal.

if (!Page.ClientScript.IsClientScriptBlockRegistered(submitRedirect))
            {
                StringBuilder sb = new StringBuilder();
                sb.Append("<script>");
                sb.AppendFormat("var oldSubmit = document.getElementById('Form1').onsubmit;");
                sb.Append("function mySubmit()");
                sb.Append("{");
                //Your code here
                sb.Append("return oldSubmit();");
                sb.Append("}");
                sb.Append("document.getElementById('Form1').onsubmit = mySubmit;");
                sb.Append("</script>");
                Page.ClientScript.RegisterClientScriptBlock(GetType(),
                    submitRedirect, sb.ToString());
            }

Thanks to http://forums.asp.net/p/1011848/1354154.aspx for this tip.