sure it can come in handy, there's plenty of stuff in bio eng.
since being a doc was your first goal, i think a eng. study along biological lines would fit to your interests. 

i know a guy that ended up in replacement hart valve development & production, trough engeneering, so it can still be pretty close to the initial goal if you specialise into the right directions

 

My suggestion to these types of questions is to make sure you're going to like what you're going to do for the rest of your life. If you don't know what you like right now, you still have plenty of time. I didn't know exactly what I wanted to be until my junior year of high school. Just involve youself in the various clubs your school has to offer (if your school has things like DECA, FBLA, JSA, etc.). If you don't like them, then just don't show up to the meetings anymore. 

People are always going to tell you to become a doctor, lawyer, engineer, etc. because those are the people that society associates with money. And since they have money, they must be healthy, and since they have money and they are healthy, they must be happy. However, if you follow one of these careers and you don't love doing it, you'll probably end up pretty miserable.

Don't worry so much about sat, act, gpa, or ap. Involve yourself  in volunteer opportunities at places like your hospital, the library, nursing homes, or your firehouse and dedicate some of your time in high school to that. Sure, colleges care about grades and scores, but they also care about the quality of the individual. If all you have to write in your college essay are your struggles with school and SAT scores, the college adm officer is going to think you stare at books all day. Colleges want people who will contribute to the culture and life of the campus. On the other hand, don't completely neglect your studies or grades either. 

If you don't know exactly what you want to be, involve yourself in as many places you can. You'll find out eventually.  There are also a lot of good books that help you learn a lot about yourself. I suggest The Alchemist by Paulo Coelho. 

However, if you want to become an engineer, I definitely suggest taking as many math courses as you can in high school. (I took alg1, alg2, geom, and pre-calc on the honors level and calc and stat on the ap level) If you apply for an engineering program, the first thing colleges will look at are your math courses.

  What is it that you wish to do as an engineer?

  I am a physician, did all that crap you mentioned. One of the guys I train with is has a Ph.d in bioengineering. He had a desire to work in medicine but did not like the idea of the people contact or medicine, but really liked the idea of working with the human body. We have worked on several projects regarding bio implant materials for bone and tendon repair.

 Bio engineering is a great field, a lot of growth in it, but it is going to be a little more narrow in its field availability than say mechanical or electrical engineering.  I see no reason not to add as much engineering classes as possible at this stage until you find what field of engineering you think you want to work in.

I had a similar path as you and ended up getting a Ph.D. in Immunology.  Work in pharmaceutical development now.

You may want to look on the Internet for a Biomedical society for your country or region and look for one of the current Board members to email and ask them for advice and other people to contact to see if they could provide some guidance

ignoring that you picked a really bad place (official forums for a free online game) to ask this:

You're in high school. If you're doing well enough to get into whatever college you want and you aren't way behind your grade level you're fine. Don't worry about it, take classes you're interested in. Same thing for undergrad, even. AP classes are nice, but hardly necessary. Other than that, once you're in college the high school classes you took mean nothing. This doesn't mean you don't need to take lots of math and science, but you won't hurt anything by taking a class that doesn't say "engineering" in the name. Not even in college.

You might even change your plans for after high school, and it won't hurt you. There's no reason taking a few classes in high school will stop you from being a doctor.

If you want better advice, look for people in your area who work in the fields you're thinking about, or look up a university near you and find people there. Even if they can't help, someone like your doctor or an engineer you know probably knows someone who can.