Tank does far more than smooth pulsations. It allows compressor to shut off for awhile now and then. It allows the regulator to work better, with less effect on the compressor. The tank itself settles out some water (tank should be drained periodically to prevent rusting.
A big tank allows pressure to build up, the compressor shuts off, and you can airbrush for quite awhile before compressor comes back on.
Now, even though the tank and its pressure switch control the pressure a bit, there is a range, with a high and low limit. The compressor is shut off at the high limit, and stays off until the tank drops to the low limit. This range is too much for good airbrushing, so having a tank doesn't eliminate the need for a regulator. However, many tank-equipped units already come with a regulator (in addition to the pressure switch).