If you let the ashes get to the keyboard, it can.
A quick search in google says it can (I got curious too, my instinct says it can but I want to be sure.). An article says it can let tar to build up in sensitive components. It's best to keep the smoke away from the air intake of the cooling system. It also says that cigarette smoke can speed up the corrosion process of metallic parts in the computer. And something about the smoke making surfaces sticky and causing dirt to stick.
I haven't heard yet of anyone destroying a computer with cigarette smoke but i think it's best for heavy smokers to try to smoke a bit farther from the computer