When you fill your antifreeze, you should be careful to fill it only to the FULL mark. The reason for this is that fluids expand when they get hot. Not a whole lot, but some. Filling only to the full mark will guarantee that when the fluid heats and expands it will not overflow. There are two things to expect when you overfill the fluid. (1) When the fluid overflows, it will flow into your engine compartment and also onto the ground which can make a mess on your driveway or garage floor. (2) The major problem when the coolant flows onto the ground is that the coolant, which is a chemical called ethylene glycol, has a sweet taste and dogs and cats seem to be attracted to the taste. Unfortunately, it is highly toxic, and will kill your or your neighbors pet. Regarding the prospect of damaging your vehicle by overfilling, it won't happen. It'll simply make a mess. As a matter of safety, NEVER open the radiator cap except when the radiator is cold. The coolant is under pressure, which allows the coolant to operate above its boiling point which lets the coolant transfer more heat than it would at lower temperatures. When the cap is removed and the pressure becomes atmospheric pressure, the fluid will falsh to a boil and spew hot steam and fluid like a geyser.
When you shut the engine off after running it, any excess will blow out through the overflow tube onto the ground.