I don't think so. It is just something that people who want others to have children project into childless people with pet. It is something to invalidate/insult childless people with. Or childless in general. And occasionally to those with one child and pets.

I have never heard childless person say that they have pet instead of children. They don't have pets instead of children.

They just don't have kids and have pets. Not as replacement tho.