Yes, the honors programs doesn’t influence hiring directly, but it does influence opportunities (= can lead to better jobs indrectly thanks to having access to research+ funding + conference funding, to better advising, to special internship offers, to special “networking” events…) as well as, greatly, learning comfort during the first two years. This latter point should not be underestimated when attending a public university where there have been funding cuts, or where funding was weak to start with, or where there are many thousands of students. Priority registration is also a great perk that can make the difference between a good or bad instructor, a favorable or unfavorable time for an essential class, freeing time up for a one-day-a week weekly internship. However the situation should be assessed in comparison to the actual benefits the Honors College offers and your own goals. Honors Colleges would be especially beneficial to premeds, for instance (more support, etc) but perhaps not as important for engineering students (who already have peers who have good academic motivation.)