Is the line is necessary for the balanced star- connected load?

I think you probably mean is a neutral conductor necessary for a balanced star-connected load? If this is what you mean, then the answer is no, it isn't, as the phasor-sum of the phase currents will equal zero. Often, though, it is difficult to achieve a balanced load, so a neutral is then necessary, as it is needed to provide a return path for the unbalanced current -without this neutral, the phase voltages would change and become unbalanced.