Actually it's the opposite.
More people => more demand for production => more efficient production => cheaper groceries
Discussion
Economically sure. Ecologically is the question. According to the podcasts I've heard, they basically say if everyone was a carnivore, we couldn't feed everyone. I don't know enough to be sure what's true.
Have you heard of Holistic Planned Grazing? In grasslands (a huge chunk of the world), enormous numbers of cattle are used to regenerate the ecosystem, reverse desertification and increase biodiversity. Holistic Management and cattle are the answer to save the planet. We literally need to increase the number of cattle a thousand fold! To learn more look at savory.org and watch Alan Savory’s TED talk.