Is Chemical Engineering a good pathway to Biomedical Engineering for graduate school?
If you want to get into a biomedical engineering program in graduate school, chemical engineering is not a bad option. You would of course probably have better luck if you majored in biomedical as an undergrad as well, since your coursework would more directly prepare you for those programs.

A couple of things to note though:

There is a (big) difference between bio-medical engineering and bio-chemical engineering. Biomedical engineering is more closely related to pre-med and materials science than to biochemistry. That said, bio chem courses probably wouldn't hurt you, but if you have the option, taking real biomedical engineering courses as electives (or as a minor) would be better. For bio-chemical engineering, these days regular chem E programs almost always have at least an elective component in biochem engineering, and often times departments are called "Chemical and Biological Engineering" due to the similarities. In other words, chemical engineering undergrad degrees are very well suited (and possibly over-prepare) you for biochemical engineering graduate work.

The other thing to know is: the real secret to getting into a good graduate program is to get research experience as an undergrad in the field that you want to work in. This demonstrates to the acceptance committee that you meet the two main requirements PIs have for grad students:


You are interested in the subject.
You have the aptitude to actually accomplish something. 


A chemical engineering degree demonstrates aptitude on its own, and as @rch mentioned, is a pretty good "fall back" plan in case you change your mind later (although chem E is a tough major if it's just a fall back plan - I would not recommend it unless you really like chemistry and physics and could imagine working in a chemical plant, since that is likely what you will do if you "fall back" on it).

The problem is going to be that lots of other people will be able to demonstrate aptitude, with degrees in biomedical engineering, materials engineering, chemical engineering (lots of them get into biomedical later), pre-med, and other stuff that is just as well suited. In addition to aptitude, a lot of them (if not most of them) will also have research experience through undergrad projects or internships. To be competitive with them, you will want some as well.

The best easiest way to get research experience as an undergrad is to find a professor who is working on something you are interested in, and volunteer. Many times they will have paid positions specifically for undergrads, but if you can put in volunteer hours and are reasonably good at communicating, managing your time, and getting things done, most professors would be happy to put you to work for free. If you can manage to get a publication before you finish your undergrad degree, you will have an excellent shot at getting into the school of your choice, provided your GRE scores and grades are good (another reason to carefully consider chem E - not an easy major).

Another option is internships, although a research internship carries more weight in grad school circles than a regular old "gets the coffee and fills out spreadsheets" internship. They are much harder to get, but usually pay pretty well, so it is definitely worth trying for one.

The main point I am trying to make here is - major in (almost) whatever you want, but if you want to go to grad school in a particular field, get research experience in that field as an undergrad. Go for paid work first, but be prepared to volunteer if you have to, at least for a semester. You can quickly turn a volunteer position into a paid one if you do good work. Work experience also goes a long way toward getting you a job if you don't end up going to grad school. I'd put your odds of getting a good job with a biomedical engineering undergrad degree with experience at higher than getting a job with a chemical engineering degree without experience, especially these days.

Also, just so you don't think I'm trying to talk you out of a Chem E degree, Chem E was my major (BS, MS, and PhD) and I really liked it. If I didn't like chemistry and physics so much though, I probably wouldn't have made it through.