Go for it- the link identifies a program that does exist. There are no honors courses in engineering per the link. But the needed courses and credits mimic those required for the L&S comprehensive Honors degree. Easy enough to do for the well rounded student. I did it for my Chemistry major eons ago. The Honors version of breadth courses means a good academic peer group of classmates and there are some great science Honors courses you can take for your engineering major. You still take the same engineering courses, this substitutes/adds those nonengineering courses to your education.
I am pleased to see this program since it acknowledges that some engineering students are good in many areas, not just STEM. It does require some planning so you find and take Honors versions of your breadth requirement courses early on in your college career instead of needing to load up on them later.
btw- do this because you love learning, not because it will increase your job flexibility in the future. Employers will not look at which courses you took, nor will your major always make a difference. Do it for YOU. You will benefit from better classes most likely, instead of being one of the masses taking a course to get requirements out of the way. No matter what your major it alone does not define you. Taking arts and literature classes are helpful when you attend plays, concerts and art exhibits decades later. The Honors designation is a perk that will always be on your diploma. Taking courses for Honors will also add to your abilities, likely improving your job prospects simply because you are used to thinking/going beyond the norm.
When the time comes spend some time outlining a likely four year plan to include the needed courses. This means selecting Honors L&S courses that fit a schedule and seem interesting to you. You can always change your major or drop the honors plan if you want to later. Find out if the honors versions of freshman courses such as math, physics and chemistry fit your goals. Math may not because of the theory instead of problem based approach. That’s why advisors are there when you plan your schedules.