"planned major" role in admission to elite schools?

It depends on the college. Some colleges, such as MIT, do not admit by major. Then again, everyone accepted to MIT is probably capable of majoring in anything and making a success of it. Other colleges DO admit by major. Personally I consider it important to get a direct admit to your department of choice in those cases. While it is usually possible to switch to something easier, it can be very difficult to switch into an “oversubscribed” major, usually CS or engineering. It is possible for students to get into their college of choice but be shut out of their preferred major. At some schools, it is much more difficult to get into the CS/engineering departments than into the college as a whole.

Bottom line is reseach carefully, have several backup plans, and apply to a good mix of reach, match, and likely schools.

Edited to say: I realize you said he is not a CS guy, however universities often have individual mixes of STEM majors among their colleges.