Considering the fact that boxers use hands all the time.... yes they can most probably punch through boards. I never knew Ali had a lighter bag either. Figured that after punching all them other boxers a standard bag would be fine for him.
My guess would be no. Boxers train to dodge punches and throw combinations rather than focus all of their energy on one punch. Breaking a board requires extreme mental power which is what martial arts like karate focus on; something most boxing clubs do not.
Of course any person with some form of strength can break through a board and breaking it by accident has nothing to do with boxers. But the question asked was if boxers can punch through boards(plural) and he also referred to breaking them as easily as a karate master could like they show on t.v. Breaking multiple boards is what martial artists test for true strength and focus and compared to a black belt in karate, a boxer would more than likely not break nearly as many boards. It's not what they train to do.