It sounds like you want to HIDE the customer login (auth box) ONLY if the customer is not logged in, yes? It is not advisable to hide the box for a logged-in customer.
If so, do this:
Code:
{if $login ne "" }
{include file="customer/authbox.tpl" }
{/if}
This will only display the auth box IF the customer is logged in.
Hope this helps.