No it will not damage the ignition system.
The old regular auto style system with a belt driven distributor with points, condenser and ignition coil can damage the ignition coil if you leave the key ON.
If the points are closed current will flow through the primery winding in the coil and maybe damage it.
The smaller Chrysler/Force OB such as the 45 and 55Hp with battery ignition system will maybe damage one ignition coil if leaving the key in ON position.
As they have one points for each cylinder and one points will be closed.
Many coils have been fried at those engines because of left the key in ON position.