Would the damage still have occurred?
Maybe. Maybe not.
There are not a lot of absolute laws when it comes to lightning.
Sometimes the lightning strike hits a ground wire that is above the "phase" wires on the utility pole. When that happens, the power of the strike is conducted to something that is attached to ground. However, during that fraction of a second, it can raise the voltage on the ground wire to go from Zero to a Zillion, and then drop back to Zero.
Sometimes the lightning protection in your home electrical system will protect you partly from voltages from phase to ground or from phase to phase. But when the ground itself gets raised up to 3000 volts or something, the protection can't handle it, so your fragile electrical stuff gets zapped. Sorry.
There are better lightning protectors available.
–B.G.–