A new study says no, adding to the confusion:
This paper contests the results of Cohen and Wang (JFE 2013, CW) that staggered board (SB) lowers firm value, based on the stock price reaction to two Delaware court rulings in the case of Airgas (2010). The first ruling weakened SB’s potency and the second restored it. Contrary to CW’s findings of a significant negative effect of SB on the value of affected firms, we find no such affect which is statistically significant for both their sample and for a different sample. Also, we find that firms that de-staggered their boards realized no improvement in their return on assets.
Amihud, Yakov and Stoyanov, Stoyan, Do Staggered Boards Harm Shareholders? (November 5, 2015). Available at SSRN: http://ssrn.com/abstract=2686902