This is really a teacher decision–whatever works best in your classroom. Some teachers do let the students take all their familiar books home to read. Other teachers let the students choose one or two books for their practice at home. Still others let the students take just their books read in strategy groups or individual conferences and then they are added to the book boxes.
You don’t need to send the box itself–using baggies or another type of bag can serve for the take-home books.