I get dime and penny boxes from the big chase in my neighborhood sometimes and don't even have an account. Just walk up and say "I need to get a box of dimes" and they usually give it to me no problem.
Sometimes i get smaller amounts at the other chases around here, but they usually don't have boxes. Although when I asked for halves she said they don't have any but could order some (i didnt tell her i dont have an acocunt, i just said i didnt want to order.)
All banks are different so just try it out and see