There are plot-driven stories and there are character-driven. If yours is plot-driven, readers won’t expect “full-bodied” characters – but they still have to have some level of interest in them. And you need to be careful that any character is not truly “flat” – nobody likes to read about cardboard characters.
As to the character’s past, even in character-driven stories their past is not always necessary to know. Often a little “mystery” works as well as a biography. I like to know enough to understand why a character acts/reacts the way they do – but I also prefer that information to come when and where it’s needed, and not in one big blob of info.
Like Rob said, keep the reader turning the page. If either the characters or the plot makes the reader wonder if it’s worth continuing, you’ve got some work to do.