As long as they have water and sugar water they can easily survive for a week. In the worst case they'll eat some of the brood.
My Camponotus (~30 workers, extremely well fed) had no issue being alone for a week. They had sugar water (Sunburst because it doesn't mold), a large spider (which they ignored) and dry fish flakes (which they ignored as well). When I added new food after my return they had 2 workers out foraging instead of 1 but that was all. They didn't develop a lot while I was away either, probably due to the cold weather (was kinda rainy at around 20°C).