Would computer science people really be that worthless? There's really no reason to automatically assume this disaster would destroy computers unless it's some kind of massive solar flare that kills every electronic device on Earth. In any other case people would probably still need people to fix and maintain computers. Even if the networks go down computers can still do shit. They can make calculations faster than people can, they can be used to make records, keep people entertained, etc. And there are probably still people who'd be able to get the networks back up, in which case it would continue working as a communication system.
It would depend largely on what kind of social structures emerge in this post-apocalypse world. People without practical skills would be dead weight at first. But perhaps there might be some groups with the foresight to keep professionals alive?
Accountants, engineers, scientists, programmers etc might be legitimately useful in a large and well organized enough group, but what are the odds of one of those arising?