I was wondering about that. It is surely a confusing concept. I wonder if the original series also has it.
I didn't know if I should post on the rebuild category or the anime category, because it includes both versions of evangelion. Sorry for bad english.

It is not, no.
There's some things in the early drafts that the Curso of Eva has very clearly evolved out of, but nothing of the sort was included in the final product.

In the sense of not growing up, no. One can make all sorts of reasons outside the narrative why it was added in the rebuilds.

But there was a more abstract sense in which once inside the secret, you could never escape the burden of knowing.

Yes, you can probably say that for most of NGE it applied to the kids too. While the curse of Eva per se as it exists in the rebuilds is handwaved as a side-effect of piloting, or the LCL, or something vague to that effect, in NGE there always was a pretty evident metaphor for the Evas as somewhat infantilizing, of the entry plugs as metaphoric wombs, and the maternal associations and imagery were all over the place. Shinji and Asuka and Rei are in a way freed from the Evas. Shinji says goodbye to his mother and father and makes peace with the latter, Asuka realizes she wasn't abandoned, but likewise has an instrumentality of her own and decides to move on to the big bad world. Rei becomes a god thingy though we have discussed before that it doesn't preclude her from attaining humanity either.

In NTE we have a brief mention of Yui being the "control mechanism" for Eva 01 and... that's kinda it? While we can (probably?) assume the same for Eva 00 and Rei's splintered soul (inb4 it's akshually Naoko), there's no Kyoko for Unit 02, so, I'm not sure what we're supposed to draw there, except perhaps Yui in 01 was retained for more narrative purposes. Many maternal scenes are removed, some aren't, so we have to rely more on the Curse of Eva in a more meta sense.

Throughout the years of fandom, many old theories and particularly doujins (and we know Anno draws from at least the latter) played with this idea. I recall one non-H doujin had the pilots not aging too, and another, uhhh, had it dissolve their pubes indefinitely, specifically due to the effects of LCL.