People who have been up this month have been using them. I don't think the worst spots will be clear by that time. The worst places are the top of the switchbacks -- that one last long section that heads over to Trail Crest, and at the cables.

When you go, if the conditions are good (it is warm), the snow will be slushy and regular boots will grip well. But if it is cold (as if you return from the summit later in the afternoon), the snow could freeze up, making the same sections treacherous.

Look for the Ice Axe Use links in the "Links to important Whitney information" page in the Reference forum.

Here's a picture posted by Kurt Wedberg, who runs the SMI guide service, from this past weekend, looking from the summit to the switchbacks:



Kurt W's SMI pictures link:   Mt Whitney May 9-12 2013