Without ice, an insulated compartment in your breast pump bag will simply keep your pumped milk at the temperature at which you put it in there, which is likely to be lukewarm, unless you refrigerated it first. If you'll be returning home within a few hours, there's no need for ice, but if you won't be using or refrigerating the milk for longer than four hours, it's safer to add ice packs to be certain the milk will stay fresh.