NO, on the older radiator systems that were filled by the radiator they were only filled just above the top edge so there was a big space above the water level, this is your expansion tank, hence why they also had a tube leading from the rad cap in case they expanded too much due to being overfilled.
So plumbed correctly there is no reason you can't do without one, as the rad has one, may have to bleed the system though by disconnecting from the highest pipe/point till air free water comes out, expansion tanks took care of the de-gassing owing to the position of them being the highest point, or at least their bleed hose.
tabetha