A big heavy cooler can and almost will always bend the board, however as to if it will damage the board, not likely unless it has a really crappy mount.
As long as it has a nice backplate, it should be fine.
A PCB can bend a lot without being damaged.
EDIT: If you are concerned about the weight on the board, my recommendation would be to go with an all in one liquid cooler, as that will put very little weight on the motherboard.
Something like a coolermaster or corsair cooler will work nicely and provide very good performance.