Idle solenoid comes on with key, and sets throttle plates at slightly open position for idle air/fuel mixture. When is shut off, idle solenoid retracts, letting throttle plates close completely, preventing "dieseling", where car keeps sputtering after key is off (heat in engine is enough to ignite an air fuel mixture in intake). By closing off throttle plates, less air can enter intake, so air/fuel mix won't self-ignite.
Do you need a solenoid? Depends if you get dieseling after turning engine off... usually slightly modded engines won't need it... disconnected vacuum advance, bigger cam, different intake, larger valves, etc...
Only one way to find out.... 8 )