[mad=dog]

A mage cannot replenish his spells without rest. I know, I know, the game allows you to do that, but that is besides the point. The rules does not and it is a flaw in the game.
They made an error in one class, but didn't repeat it in another. In shorter terms - no you cannot replenish your spells without rest.

... actually come to think of it I may be wrong here. There is a bug that allows you to cast Simulacrum indefinately from Vhailor's Helm. I cannot recall if Shield of the Archons allows you to re-memorize spells. If that is the case then you can technically replenish your spells without sleep.