No, a classic sandbox is having all of the areas, NPCs etc. already set. The PCs then can wander freely and encounter them, but they are constrained by what the DM has placed.Odd, I thought Sandbox Style was just doing what the players wanted. The idea is the players lead and the DM follows, right?
Now, done well/properly the PCs will act as dominoes/ripples and much of what they do will change how the surroundings respond so it will be a very different experience depending on who the PCs are and what they do.