What you can do is hook into the validator and assign a new evaluate method, like this:
<script type="text/javascript">
rfv.evaluationfunction = validator;
function validator(sender, e) {
alert('rawr');
}
</script>
rfv is the ID of my required field validator. You have to do this at the bottom of your page so that it assigns it after the javascript for the validator is registered.
Its much easier just to use the CustomFieldValidator and assign its client side validation property.
<asp:CustomValidator ControlToValidate="txtBox" ClientValidationFunction="onValidate" />
<script type='text/javascript'>
function onValidate(sender, e)
{
alert('do validation');
}
</script>
Check out the documentation here and here.