Lael Brainard seems to have done ok with her CSS background.
https://en.m.wikipedia.org/wiki/Lael_Brainard
As you can see from the description of the major, you would take Econ classes outside of the CSS specific offerings.
http://www.wesleyan.edu/css/about.html
I would imagine that if you have your eye on grad school for Econ, you can craft an appropriate program as a CSS major.
I’m not saying you shouldn’t ask here, but your questions are also excellent questions for an interviewer, an admissions rep visiting your school or, assuming you apply, the AO for your region.
FWIW, when I was at Wesleyan in the early 80’s, I had a number of friends in CSS. It was a very impressive program and I assume it remains so. Many of them went on to law school, but that doesn’t mean it’s the only thing people were prepared for.
I can highly recommend classes with Rich Adelstein and Don Moon.