No, because production would then shift towards fruit and vegetables to meet the demand. We dont live in a static zero sum universe.
Just playing devil's advocate here. Are you sure there is enough arable land and healthy topsoil to meet demand? Is it feasible or practical to create arable land and topsoil? If the answer to either of these questions is "I don't know" then I maybe the economics here aren't favorable to your argument. Again, just devil's advocacy here.
We might start farming on protected land, replace the crops who are now getting included less into people's diets as a result of increased fruit and veg consumption (e.g. less grain intake could result), we have fertilizer, and the more that demand spikes and the more the prices increase, hydroponic solutions and greenhouses become more and more viable, as does increased genetic engineering research.