“Kycoo the Ghost Destroyer” will prevent Machines in the Graveyard from being removed from play for “System Down”, but Machines on the field can still be removed from play by its effect.
If your opponent has no Machines in the Graveyard and no Machines on the field, you cannot activate “System Down”.
If “Heavy Mech Support Platform” is equipped to a Machine when “System Down” is activated, the equipped monster is removed from play but “Heavy Mech Support Platform” is just destroyed and sent to the Graveyard.