I think "route" was the wrong word. If you set up CNAME in github.com/jdan/jdan.github.io to jordanscales.com, then accessing jdan.github.io/cleaver will result in a request to jordanscales.com/cleaver.

If your repo github.com/jdan/jdan.github.io has a cleaver subdirectory, then it will direct to the directory in the repo (masking the gh-pages branch). However, if you do not have a cleaver subdirectory (which is the case at the moment of writing), the gh-pages branch will be visible

What do you mean that changing gh-pages on a project doesn't change anything? The github pages for the project will continue to be available, but they will be available at www.example.com/project instead of username.github.io/project.