It is my understanding that BME positions usually require an advanced degree. If you are looking for an engineering degree to “fall back on” then it may not be the best course. Please understand I’m just a dad with two kids in college and one who is an engineering major at Purdue. My second D want to be a Physical Therapist which requires undergrad course work similar to a pre-med major. I would say the engineering degree is definitely more challenging. The level of math and physics is definitely higher than pre med. In my opinion the courses require different strengths. The engineering is very conceptual, while the biology and anatomy and physiology is very memorization based.
I am not an engineer myself. Some of what I’ve said is through the experience my D has had at Purdue and from my younger Ds pursuing an allied health degree, the rest is information gleaned from CC. I would say that you will likely be discouraged from double majoring in two different colleges by Purdue. I am sure there are a number of engineering majors who might have similar ideas concerning med school and Purdue could work with you on arranging a schedule to fit in those courses. Good luck.