If we all ate vegetables and crops, wouldn’t we need more pesticides?

Yes

No. Setting aside the question of whether pesticides are needed at all, if everyone were vegan we would use less pesticides because we would actually grow less crops. Meat animals all eat plants and they convert them into food very inefficiently. On average, a farmed animal has to eat 10kg of plant protein in order to make 1kg of meat – in other words, if the same land was used to grow crops for people to eat, it would be ten times more productive. To put it yet another way, 90% of the crops we feed to animals are wasted. If we didn’t eat animals, we wouldn’t need to grow those crops or use chemicals on them.