A stuck-close or clogged EGR can increase engine temperature. If the problem leads to detonations, it can damage the engine. So it's possible. This problem is more common with EGR cooler failures when it causes loose of coolant. I personally wouldn't recommend deleting the system. It may lead to engine overheating, increase emissions, and driveability issues.
Aftermarket head gasket repair products can do the trick if the damage is not extensive. However, the repair might not be permanent. That said, I've known of people that have some success with Blue Devil and Steel Seal. You may want to do some research and see which will work best for the type of head gasket you are using in your particular application.