Starting off here I'd like to say that yes, we will win. Human suffering will eventually end, because probabilities add up over an infinity of years, and eventually all humans will all die out. I can't say the same for alien species, since if there are multiple universes continually being brought into existence, then I must say that as antinatalists, we are well and truly screwed.
But on a shorter scale of time, are we alright? Will things go alright for us? Certainly I'd wager that most of us will be dead by the time antinatalism becomes anything that is in the vocabulary of most people, but as for whether or not it will have any influence on their genitalia, I can't really say. The problem with antinatalism is that it is so absolutely appalling in the eyes of most people out there who value their lives, and most influential people are generally of this kind, that it is unlikely that many people will come round to seeing things our way. Yes, there'll be a few converts here and there, that's just a matter of chance and our increasing publicity among economic and philosophical circles, but essentially there is such a large mental barrier blocking off rational discussion that I doubt that without widespread understanding of the arguments of antinatalism would it hold any kind of political power. As a personal anecdote, I'd like to say that the people I talk to in school probably know the arguments for antinatalism at least as well as I do, YET STILL CANNOT EVEN CONSIDER THE IDEA. As long as it is so firmly entrenched within people's minds that having children is a right, that suffering is necessary for life, and that that elusive deity called meaning can be acquired through creating a non-consenting human being, there is little hope for antinatalism to spread.
But I do think that even if it won't become necessarily popular enough in our time, there will be certain people susceptible to its ideas without much resistance - just as most of we, who frequent these blogs, came to understand antinatalism without much resistance. So while we may become the new pagans of our time, or satanists or what have you, I'd bet that the antinatalist population will grow significantly soon enough (ironic as that is). Whether or not things will work out only time will tell, but for the moment, fittingly, I am quite pessimistic about this whole affair. But I would say that the difference between now and Schopenhauer's time is simply that we now have the internet - now our voices are not suppressed, and anyone interested can simply search for us, and find us they will. And moreover, if we adopt children, we may actually defeat the whole 'natalists will outbreed us there is no point' argument. So there is SOME hope, but not a whole lot. Though I guess most of us being pessimists here, those are the kind of conditions we're used to. Have fun and take it easy, never forget to look after your unborn children. Bye for now.