Yes. But if an incoming CEO has a lot of political capital, they can try and demand that certain board members leave as a condition of taking the job. It's unusual, and takes an unusual person to pull it off, but it happens. (For example, this is what happened when Steve Jobs was made interim CEO of Apple.)
Mayer is a big coup for Yahoo, and the investors may back her if she wants to clean house with the board, but I wouldn't necessarily expect it to happen; it's unclear if Mayer really sees the board as part of the problem, and as Mayer is coming from outside of the organization, she may lack the close ties to other Yahoo execs that would be necessary to pull such a move off.
Mayer is a big coup for Yahoo, and the investors may back her if she wants to clean house with the board, but I wouldn't necessarily expect it to happen; it's unclear if Mayer really sees the board as part of the problem, and as Mayer is coming from outside of the organization, she may lack the close ties to other Yahoo execs that would be necessary to pull such a move off.