This is indeed possible on an unrooted S4:
public static boolean setTransparentNotificationBarTouchWiz(View view) {
try {
Field field = View.class.getDeclaredField("SYSTEM_UI_FLAG_TRANSPARENT_BACKGROUND");
Class<?> t = field.getType();
if (t == int.class) {
int value = field.getInt(null);
view.setSystemUiVisibility(value);
return true;
}
} catch (NoSuchFieldException e) {
} catch (IllegalAccessException e) {
}
return false;
}
My thanks to Kevin @ TeslaCoil for sharing this flag with me.