No, because DALL-E is only doing statistics, so training based on other DALL-Es doesn't add anything fundamentally new to the dataset.

I want to point out that most people actually get creativity wrong. It's an unfortunate truth that most of the "creative" tasks in the field are largely about association, perhaps with some errors, either intentional or not. It's really just all about querying (finding solutions), planning (arranging found solutions), and executing (apply the solutions accordingly). Human can perform these tasks both intuitively and logically, but, people normally mistake the intuitive approaches as "creative", even though it does the exact same things as logical approaches.

Let me give you an example.

Say, you're a designer and your client wants you to draw a bear drinking coffee. Unfortunately, that's usually all you get in reality, just like queries for DALL-E. You should figure out which kind of bear it is, which style it is drawn in, which type of cup it's holding, where the heck the bear is, blah blah...

You naturally start with surveying, probably by googling "bear" and "coffee". You browse through different types of bear and different types of coffee cups. Perhaps, you may have some specific images already in your head if you've drawn many enough bears and cups of coffee. In either cases, you come up with some base materials.

Now, you choose materials to use: which bear to use, which cup to use, which background to use, etc. You can use your gut feelings, of course, but you also can take numerical approaches and sort them by popularity on the internet, or by the ratings from your clients if you have data, etc. Anyways, you choose materials based on something.

After that you lay materials out - do mind that layouts are also subject to surveying and sorting - and draw a white bear drinking coffee in a ceramic tea cup, relaxing on a hump of snow. Perhaps near an igloo, because it's snowing! Since you got all your materials ready beforehand, this part is mostly about blending them into one scene.

... and let me ask you here: is this process really creative? I mean, this whole things sounds more like engineering to me. It's a highly logical process, with some room for incorporating intuitive association. Perhaps it's a lower-tier of creativity, if one really doesn't want to change the view.

..

So, what on the earth is creativity?

Since I'm not authoritative here, I can only humbly suggest it's an ability to push the boundaries of the (base) reality. If association is an exploration inward to find what's known, creativity is an exploration outward to find what has never been known. It's a trip into an virgin territory, which certainly requires meta-perceptual ability to conduct.

Anyways, so, if an AI is creative, it should be pushing the boundaries of what it's supposed to be doing. If the AI generates images, it should come up with a completely new style of art, new characters that no one has ever designed, etc. It should be contributing to the human society by introducing new cultural elements.

However, in case of DALL-E, it's just an external association engine. It allows untrained people to query, arrange, layout, and stitch image materials, though customization is close to zero. It's users are currently trying to push the boundary of this AI, meaning it's the users who are creative here. DALL-E itself is a tool for actual creative activities.

Thus creativity has never been challenged, unlike what enthusiasts love to claim. The whole hype here is rather a cheap word play.