Vee1 - the mechanical mixing unit that Jack describes will compensate for a certain amount of torque-induced yaw - as the collective is raised the mixing unit moves the anti-torque (power) yaw control. It is effectively putting in left pedal for you as you raise the lever (assuming counter-clockwise rotation of the rotor when viewed from above). Other mixing of collective to cyclic can offset some effects of flapback (pitch) or Tail rotor drift (roll).
However, in order to lift to the hover with feet off the pedals, you require a heading hold function which is the higher mode or outer loop autopilot function - something beyond the capability of a SAS.
In simple terms, a SAS uses series actuators in the control runs (fast speed but limited authority) but SAS only senses a rate/displacement error (using the Vertical and Horizontal Gyros) and opposes it, improving the handling qualities of the helicopter by damping the inputs from the pilot. When the series actuator gets to its limit of travel (usually 10%) it can't go any further (saturation).
The autopilot needs to be able to re-datum the series actuator to give 100% authority and can only do this by physically moving the flight controls using a parallel/trim actuator (slow moving but 100% authority). As this happens, a signal is sent to the series actuator to re-centre itself, thus giving another 10% authority but around a new datum. This is called open loop.
You need SAS for handling stability and rate damping but an autopilot computer for heading/ height/airspeed etc holds.
Some helicopters do without physical mixing inputs to counter aerodynamic effects and do it electronically using the autopilot computer instead.
The main reason for all this mechanical and electronic assistance is, as 212 man says, to make an unstable platform stable - it reduces pilot workload and allows him to use the helo as a tool to perform specialised functions.
Hope that helps.