I graduated with university and foundation honors. I am glad I did the honors coursework and would do the same again. It really is the difference between a run of the mill and exceptional academic college experience, but, of course, it depends on what the student puts into it and what the student wants out of it. If one is taking just one honors course a year to maintain some early registration perk, they might not derive as much benefit from the experience.
It also depends a lot on the academic department. I was fortunate that my department offers one of the best slates of honors courses, with honors options for almost all of the mandatory courses. You might see if the academic department will put you in touch with upper level honors students. They would be the best to share the value of being an honors student in that particular degree program.
On the other hand, I don't think any of the medical school admissions boards noticed. So, in that regard, I would have been better off spending my time on politically preferred resume padding activities, that is, if my sole purpose in life were to pander to politically biased admission boards. Frankly, I wonder if it is prudent to take advanced science courses beyond what the professional schools require as it can be a risk to the GPA. Don't overestimate an admissions board.
Obviously (I hope), a high GPA, especially in the courses considered by the professional school, and high standardized test scores are the most important. Race, ethnicity, socioeconomic status, gender, sexual orientation, and hometown can also be fairly influential factors, if you are able to modify any of those to preferred identifies. Honors coursework is probably mostly inconsequential, and, I suspect if there were two almost identical students seeking the last spot, the one who fought Trump on Obamacare and spent afternoons volunteering at free clinics would get the spot over the honors college student.
Pondering on it, students who enjoy the honors program should probably go into academia instead of professional school.
It's a great thing to go to school with a goal (and is a great concern that so many go to college without a clue), but it's also okay to discover your calling and follow a new path.
Good luck. Gig 'em