Not so re: engineering. I know a poli sci major,ROTC,good leader/smart kid who got a pilot slot. Now an AF Captain. But he had skills when it came to piloting.
Had a tour during my USAF career as an Air Force ROTC instructor. There is no link between engineering degrees and becoming a pilot; your AFOQT scores and physical qualifications are much more important.
One reason you see a lot of engineers in the cockpit is that the Air Force Academy curriculum is weighted towards that discipline, and ROTC (historically) awarded most of its scholarships in engineering and the hard sciences.
The last pilot to retire from active duty with multiple kills was Colonel Cesar Rodriguez, career F-15 pilot who was a business major at the Citadel. The lack of engineering knowledge certainly didn’t hamper his dogfighting skills.