Yes they do study. Automobile engineering basically is all about manufacturing, fabrication and construction of the vehicles. So this will cover electric vehicles also. Also at the same time, apart from syllabus, you can study things from your own. Complete electric vehicles structure will be based in electrical engineering but that part you can study from your side too with the help of some books by relating it with your subjects. Colleges provide a lot of opportunities to get out of OUR zone. Anyhow study material and practical exposure will be altogether different. So hopefully you get practical exposure so that you can understand it better.

Refer to the site below for more detailed information..

https://www.careers360.com/courses/automobile-engineering-course

Best wishes. Thank you.