Not a direct answer but I think it does.

by R. Proffitt Moderator - 7/23/12 5:53 PM

In Reply to: Canon Powershot 310 elph hs by chu_nicholas

http://reviews.cnet.com/digital-cameras/canon-powershot-elph-310/4505-6501_7-35023862.html seems to note that ZOOM does work in video mode but video seems to not gain many kind words in the review.

After a few reviews it's clear that no one writes the autofocus is working during video but if one zooms there is no way to do a zoom without a refocus so I'm going with yes, it does.
Bob