I don’t see how a sandbox can’t work with the idea of developing a backstory over time. Typically in a sandbox there are a variety of options the group can explore and they will slowly learn about themselves and reveal bits of their backstories as they explore the various interesting things in the region.Not a clue. I can't run a game for the "play to find out" crowd, so my pool of anecdotes is severely biased. Some randomness combined with choices and some control have worked for us, but full randomness would most likely fall very flat.
I also think "play to find out" probably work a lot better with GM's that have a planned adventure, as the finding out can be used to give motivation to work toward the goal of the adventure. While extensive backstory most likely work better with character driven sandboxy campaigns. The former would most likely not have any momentum into the sandbox, and the later would most likely clash with the GM's planed adventure.
I’m not discounting the importance of slowly weaving character specific hooks into the game at some point but that doesn’t need to happen right away when they are deciding between checking out the haunted mine, riding shotgun to protect the stage from bandits, going to the Army fort a week away to get the smallpox vaccine or hiring on as goons with the local boss.