Currently unapplied payments go into a black hole on Invoiced. I can see them on my Dashboard as an action item, but if I go to the customer page they are not visible in any way and do not reduce the customer's balance due. And if the customer logs in they cannot see that they have an unapplied payment either.
Generally unapplied payments are overpayments, and would need to sit on the customer's account until it is decided how to apply them, or if they should be refunded. Invoiced should let unapplied payments reduce the customers balance due similar to how QuickBooks Desktop functions. And it should be visible to a customer that logs in that they have overpaid an invoice (if that is the case), or that just that they have an unapplied payment.