OK but I think he is in the opposite situation - he has a valid visa but has lost his ID. Sounds like you had your ID but your visa hadn't been approved. The visa is more important than the ID.
But sure, he can apply for his replacement ID now and get a temporary paper ID saying that his replacement card is being processed so actually he will have 'ID' anyway. He just won't be able to use the thumbprint entry gates so will need to queue up at the desks.