Childbirth after the event in Childhood's End

Question

In Arthur C. Clarke's Childhood's End, after the event where the children of Earth

transformed into the nascent, telepathic hive-mind that would one day join the Overmind,

... would all new children born also have been affected?

It's said in the book that no new children were born, because nobody saw the point of procreating any more. I always took this to be a part of the book's overarching theme of species-wide endgame, that humans would never go farther than the kids already had anyway so we might as well all pack up and die. But I've heard many people say it was because any new children would just be exactly the same as the current ones. Is this ever explicitly stated in the book, or by Clarke elsewhere?

Would human beings have been able to hitch a ride with the Overlords and keep going somewhere else?

Answer 1

To answer the first question: Clarke never explicitly says it, but Karellen and Rashaverak have several conversations, touching on this. At the end of Chapter 18:

"Enjoy them [the children] while you can," Rashaverak said gently. "They will not be yours for long."

To answer the second question: The Overlords were very clear in the book. At the end of Chapter 14, during the press conference after the stowaway was found, Karellen said:

"It is a bitter thought, but you must face it. The planets you may one day possess. But the stars are not for man."

Answer 2

In my opinion, there is no clear answer to these questions in the book.

In Ch. 23, it is stated that the Overlords could not explain why there are no more children, although Jan suspects the lack of new births was due to psychological reasons.

There had been men on Earth as little as ten years ago, but they had been degenerate survivors and Jan had lost nothing by missing them. For reasons which the Overlords could not explain, but which Jan suspected were largely psychological, there had been no children to replace those who had gone.

So, the Overlords said there are no new children, but it is not stated if these children would be "evolved" or not. We can only speculate that they would be, since this "evolution of mind" happened to many people simultaneously. From the end of Chapter 19:

Jeff and Jenny had been the first in all the world, but soon they were no longer alone. Like an epidemic spreading swiftly from land to land, the metamorphosis infected the entire human race. It touched practically no-one above the age of ten, and practically no-one below that age escaped.

About the second question: although, again the book is not 100% clear, since all other humans died before

Earth's destruction

It does not seems that Jan, at least, would be disallowed to go with the Overlords - he choose to stay on Earth voluntarily, and Rashaverak questioned him if he is sure about his choice, so it is hinted that he could choose to leave Earth. From Chapter 24:

JAN: "I shall stay, " said Jan abruptly . "I have seen enough of the universe . There's only one thing I'm curious about now- and that is the fate of my own planet. "

Very gently, the ground trembled underfoot .

(...)

JAN: "If, of course, the Earth still exists."

RASHAVERAK: "You realize that danger-and yet you will stay?"

JAN: "Yes. I have been home five-or is it six?-years now. Whatever happens, I'll have no complaints."

RASHAVERAK: "We were hoping, " began Rashaverak slowly, "that you would wish to stay. There is something that you can do for us .