What I have seen says otherwise. There's a thing about chemical agriculture: when you first implement it, you get incredible yields. Then the soil starts dying (no more acari, no more fungi, compressed soil…), and the yields slowly go back to roughly the previous levels, only this time you need all the chemicals to sustain it.
If you suddenly say "let's go organic", you're in for a disappointment: the soil is dead, the yields you get will be terrible. Indeed not enough to feed the world. Fortunately, soils can be resuscitated. One component is rotting pieces of wood, that bring back fungi. You need other things I'm not aware of, but the idea is, in 3 years, your soil is good as new. Mostly. While you now can go organic with good yields, you still have the old chemicals dwelling in that soil. It will take 15 years before you're really free from them.
With a good (or properly resuscitated) soil, it appears organic agriculture have higher yields per unit of surface than chemical agriculture. However, it requires more labour. It would seem the yield per man-month may actually be lower.
We don't need more farming surface. We need more farmers.