can you go to college majoring in bioengineering, but still be in the premed program?

Answer 1

Of course you can.

You can even major in fine arts and still be in the premed program.

Answer 2

You can major in whatever you like and be pre-med. However many medical schools are moving away from accepting Fine Art students into their classes. Biomedical engineering usually offers all the basic courses you need for medical school. Some schols such as the University of Toledo will hold sats in their college of medicine for some of their biomedical engineering students provided they meet certain grade requirements.