Unless things have changed, yes but no. You have to leave the app running, and turn off display sleep/lock so the phone is always awake. Which practically means

Unless things have changed, yes but no. You have to leave the app running, and turn off display sleep/lock so the phone is always awake. Which practically means it has to be plugged in. It's a major pain. As someone else commented, a classic example of Apple limiting background sync in the name of "stability and battery life". That has a grain of truth to it, but let users make that choice!