Even without computers. Computer Science is a damn useful skill.
Computer Science is the Science of Computation.
So in this theoretical world where technology is gone, which will mean that we won't know how to make electricity by spinning a magnet in a bunch of wires, or how to make a battery with Zink and copper in an Acid. Then sending this electric current threw some sand to make a transistor. Then we arrange these things into Not gates, And Gates, Or Gates. We seem to know quartz can vibrate so we can remake a counter.... We can save stuff with magnetizing it on rust suck on something sticky.
So the idea were we cannot have a computer made from scratch within a few years, as we already know about them and how the basic components work, is rather silly.
However in the mean time, these computer scientists can use these skills to manage a labor work force. Giving them simple jobs, aligning them so they can perform complex actions. For example in college cafeteria. I found there was a long line for the utensils, Because all the forks were group together, the spoons were grouped together then the knives were grouped together. The computer science people saw that this line was being inefficient as only 1 person was at the table at once because they almost always needed the fork. So we moved the forks, spoons and knives into clusters next to each other and were able to improve the line speed threefold.
Computer Science disciplines the mind to think of things in terms of efficiency, and patterns, as well figuring in the unpredictable actions from people, and their more predicable actions in masses.
So in this theoretical Apocalypse work the computer scientist is still a useful person in such a world.
Now this said, in order to get such an world, you will need to kill off all the information and including the smart people. So you will need to kill of all the computer scientists, engineers, and other educated people to really create such a world.