In general, questions like this often have the answer "if it sounds like a risky idea, we don't recommend you do it." Is it theoretically possible for a cuttle to live in a tank for a week? Sure. Is it responsible pet ownership? Not really. What if there is a blackout? A pump failure? A leak? Some large thing on your live rock dies and a water change is needed?
I'd say you should plan to find a knowledgeable cuttle-sitter to check in on your pet once a day, or similar.