If you aren’t careful when installing the rack, yes, your bike rack may damage your car.
Putting too much cargo on a hitch-mount rack can damage the hitch. Not mounting a roof rack correctly can result in your bike slipping off and falling on your vehicle’s roof. An though rare, your bike can swing forward and break the rearview window if you don’t ensure there is enough tension in the straps on a trunk-mounted rack.
As with all add-ons, be sure to follow the manufacturer’s instructions for how to securely and safely install your bike mount and secure your bike to the rack.