No, a headset will DEFINITELY not turn without the bearing balls
The bearing balls are what allows it to turn smoothly under load.
Try taking two pieces of smooth but irregularly shaped metal and squeezing them together will all your strength. Can you rotate them freely against one another? NO! That's where bearings come in.
Don't try to ride the bike without the bearing balls in place. You'll destroy the headset races at a minimum, you won't be able to steer, and your fork will wobble unpredictably. Get new bearing balls, they'll cost you about 2 bucks. The bottom half of the headset is the part that bears most of the weight, by the way.