Not really, not unless you slam your pc around and bang it or drop the case with the cooler mounted. Motherboards don't flex a whole lot, they typically have mounting screws above and below the socket. The longer and thinner something like a motherboard is, the easier it is to bend. If grabbing the top and bottom of an atx board and bending it in the hands it would flex pretty easily. With the mounting screws so close it effectively shortens the length of the board between the top and middle screws making it much more difficult to bend.
Large air coolers also using larger support brackets usually made of metal that press against the back of the board and spread the weight out over a larger area. The backplate moves the force of the...