At first I laughed. Then I just got kinda sad. Are we doomed to be collectively held back by a significant portion of the population with a poor education or is it possible to lift everyone?
Historically, there have been moments of very rapid literacy, so just to answer the question - is it possible?, yes. The question is more of when does literacy become relevant o everyday life, if the literature is made relevant then people will learn. This is even true on a smaller scale in the classroom, even with all the challenges of education
I really don't think genetics have much to do with the current populations' intelligence compared to many generations prior. There's simply not been enough time evolutionarily speaking to make a difference I would say. Basically all of recorded history is a blip when considering evolution on a longer time scale.
Education and a stable, fruitful upbringing is what makes smart people if you ask me.
But I'm mostly basing this on a gut feeling or a hunch, not really anything rigorous.