You don't need to be an EMT to get a job as an RN in the ICU. Generally speaking, most ICU's will hire new grad RN's. You will go through an extensive orientation with a preceptor, until you are able to work on your own. I went straight into the ICU as a new grad RN. I would suggest getting in touch with the hospital's HR dept. your considering, and ask them if they offer an orientation in the ICU to new grads and take it from there.
If, however, you still want to get to get certified as an EMT, and do that type of work while your attending nursing school
that, of course, is always an option. It never hurts to be getting experience in the medical field while attending nursing school.