This is a fascinating question. You could view NodeBox as a long-term experiment meant to answer that question. As its creator, Frederik De Bleser has a unique perspective; I hope he will find the time to attempt an answer.
My own take is that data and algorithms are to a generative artist what paint and brushwork are to a painter. Just as a good painter needs to know a lot about paint (where to get it, how much it costs, how to mix it, which hues you need to create different effects), a generative artist needs to know a lot about data (where to get it, how to make it yourself with random number generators, how to clean it, how different types of data behave under various transformations).
Similarly, a generative artist must somehow develop a facility and comfort level with algorithms, with understanding other people's algorithms, with creating her own, with developing a toolbox of techniques to accomplish various effects, etc.
So does a generative artist need a CS degree? No. But does she need "computational thinking skills"? At least with the tools we currently have, my feeling is: Yes.
I base this on my own experience in the workplace, first as a developer, then as a user experience designer. Over the years I have seen many elaborate efforts to develop new tools to empower "ordinary" workers so that they don't have to go to a developer or IT department in order to create a report or process or visualization. So far these efforts have all failed.
The reason seems to be that a certain basic set of computational thinking skills is essential to these tasks. There seems to be no way around it. No clever or magical UI will eliminate the need to decompose a problem into smaller parts, to debug, and to think abstractly in a way that seems foreign to anyone bewildered or traumatized by basic algebra.
Yet I still wonder if this need always be so. My wife is a knitter, an art form that has much in common with coding. Although she is highly intelligent and did take a programming class in college, she is not terribly mathematical and I think she would struggle with generative art as it is currently done.
Yet she is a skilled and artistic knitter. Perhaps the difference is that knitting, like painting, is entirely tangible. You touch the wool and work it with your hands. Knitting charts do require a certain level of abstraction, but in general most of the experience is direct and immediate.
NodeBox takes a big step in this direction by using reactive programming (each action has an immediate reaction) and a visual interface with scrubbable controls that engage a more visuospatial style of thinking. This creates an experience less like solving a Rubik's cube and more like shaping a pot. You can read my essay on this here:
http://theappslab.com/2015/07/28/better-ways-to-play-and-try/
So far, though, I have been unable to lure my more fully right-brained designer colleagues into trying NodeBox; it still seems intimidating to them. So we're not there yet. But perhaps when virtual reality is perfected we can make coding fully tangible. Or perhaps machine learning will enable tools so intuitive that we can create art by conversing or dancing instead of coding.
So, ultimately, your question remains open.