the actionlink helper is rendered at the server, the value of the dropdown is selected by the user at the client side
so what you can do is something like this:
<a id='badd'>add</a>
<script>
$('#badd').click(function(e){
e.preventDefault();
window.location.replace =
'<%=Url.Action("Add","AddAction", "AddController")%>' + '?accessID='+ $('#dropBox').val();
});
</script>