Most Christians would be uncomfortable having children if they knew for a fact that these children would go to hell.
Foreknowledge of infinite suffering or total failure, even if one is convinced it is not causative, would still cause the average Christian to do what they could to prevent said infinite suffering or total failure.
In this case, (the scenario listed in the title) the only thing the Christian in question could do to save this soul from hell would be to never birth it in the first place.
This hesitance to give birth is hardly something one needs the threat of hell to understand. We can completely forget religion for a second:
If, given absolute proof that your future potential child would be born with an incurable genetic disease that would lead said child to be severely handicapped and die at a young age, it's not unreasonable to abstain from reproducing. This doesn't even qualify as a hypothetical; it happens all the time.
Parents are used to operating under the assumption that they ought to do what's best for their infant children, even though their infants cannot provide input or consent. Birth itself is done without an infant's consent, but even after the fact, infants are still vaccinated. Circumcised. Fed a bunch of yucky food. Introduced to their family's faith. Ect. All for the greater good of the infant.
There is no compulsion to breed in Christianity, at least, so I've been told. Yes, I'm aware of the rather odd "fruitful and multiply" command, but refusing to reproduce is hardly unprecedented in Christianity, and it's not punished. Catholic priests exist. Monks exist. Nuns exist. Jesus exists.
And again, even if we forget religion for a second, it's absurd to think that every human must produce as many children as possible. There's no compulsion inside or outside of religion, and we are already comfortable with the notion that someone can abstain from having kids for any reason (even one's we don't relate to).
What better reason to abstain from having kids could there be than saving them from hell? Christians already sacrifice and intrude plenty in their attempts to save others from hell. And note, I'm only talking about children who a Christian parent knows, ahead of time, will go to hell. We're assuming God-like foresight and hell as Eternal Conscious Torment. I know some Christian frameworks do not grant God foresight and do not believe in hell.
For Christians who would have children they know would go to hell, surely there's a limit to the number they'd be willing to have? If so, I'd be curious about that number.
Oh, and if you need extra information, let's also assume that these hypothetical hell-bound children will die and go to hell before they themselves have any children. That's just in case you're interested in doing the whole "sacrifice my son to hell so that his seven grandchildren can go to heaven" math, though I'm told Christians reject utilitarianism.