Not in the same widespread way.
With help from charismatic prophet-types, they can go far.
There’s an ape clan in the deep south–one of the oldest Gara’u. No other non-human primates, though.
I know you’re just making a Dawkins joke, but calling him the inspiration for Ghaesh is going to give people the wrong idea. 
The one time I mentioned him was a rather strained comparison of Richards (Dawkins and Matheson i.e. the I Am Legend author). The lich lord is going to be interested in persuading you to adopt his perspective on the world, and he’s a non-theist; but I certainly didn’t have the “New Atheists” in general or Dawkins specifically in mind when I came up with him.