You miss something critical here. For that to happen that GenAI would have had to be trained on another "Ghibli".

So your question isn't whether Ghibli had an AI, but whether Ghibli had a whole time traveling machine with it.

Your question feels like asking whether Einstein, Plato, etc. were secretly time travelers and copied someone else's style.

Something that is a general problem with all GenAI is that they copy and imitate. And just like with code being messy and dumb you'll find that Stable Diffusion in pieces of art does stupid and dumb stuff. Things it wasn't trained on. You can most prominently see that in big detailed fantasy (as in not just a photo) pictures, and looking at details. While the overall thing "looks cool" you don't get the details that artists do and you notice a lot of silly, dumb and what for a human author would be a "strange thing to invest time in and still do so badly" kind of situation.

I'd argue if we had AI in the sense that it had actually understood things and it could actually show creativity, etc. the story might be different, but as of today it is unknown whether that's possible. It would make sense, just like alien life would make a lot of sense. But for both actually thinking systems and alien life we have no clue how close we are to seeing one.

Every time someone takes an unbiased look at it (and there are many papers) it is shown that there is no understanding of anything, which to be fair is far from surprising given what the "training" (which is just a term that is an allegory and something that is kinda simulated, but also not really).

There might very well be hard and pretty obvious limitations, such as to feel and express like a human you need to be a human or provide away to simulate that and if you look at biology, anatomy, medicine, etc. you'll soon realize that even if we had technical means to do so we simply don't know most things yet, otherwise we could likely make Alzheimer, artificial brains, etc.

The topic then might be aside from all the ethical parts (when does something have human rights), whether a superhuman as all the futurists believe there will be even be able to create something of value to a regular human or are the experiences just too different. It can already be hard to get anything out of art you cannot relate to other than general analytical interest. However on that side of things Spirited Away already might be on the "little value" side.

This isn't to defend human creation per se, but to counter often completely off understanding of what GenAI is and does.

One final comparison: We already have huge amounts of people capable of reproducing Gibli and other art. Their work might be devalued (even though I'd assume some art their own stuff into their work).

People don't buy a Picasso, because they can't find a copy or a print that even has added benefits such as requiring as much care, being cheaper. Einstein isn't unimportant today, because you learn about his work in school or on Wikipedia.

But your question is like asking whether Einstein's work would be without value, if he secretly had Wikipedia.