At my D’s school, honors college applications were totally separate from overall university admissions but I don’t know if that’s how it works everywhere. In a world where demonstrated interest is important, I’d encourage him to apply for the schools that are high on his list. He can always turn down a place in honors college later if he isn’t interested.
I do agree with the other posters though about doing some due diligence about the different honors program. In addition to housing and priority registration, there may be special advisors, smaller class size, honors specific study abroad opportunities, and earlier access to internships/coops which is very important for engineering majors.