Yes, one can go for a week without any solar, if battery bank is big and daily energy needs are very low. You can even go for a month without any sources of power supply other than AA/AAA batteries. Did this a number of times myself. What the OP can or want do, - we don't know.
KNOW THY NEEDS.
BFL sure does - that is, he needs no solar ;) - because his energy needs, on one hand, and location, on the other hand, make living on solar very difficult.
Energy audit is the first step with any serious solar planning. What do you want from solar system? How much energy can you live on? Can solar reliably supply this, or you needs are so high and the weather is so dark that there is no chance to have a sustainable solar? And so on. To keep batteries charged between the trips a single 100W panel could be enough, or a 120V charger, or both.