Well, normally if you have the wrong GPU, it won't even fit in socket, you would have to force it in, and then you probably ruined your motherboard if you did that.
The only other way it could be wrong is if you don't have a good enough PSU, or the wrong connectors.
So no, "any" graphics card will not damage your motherboard, using the wrong one and doing something.... really stupid, will. What is your motherboard exactly? The model name and that.