EMT and RN?

Just the license? Probably not.

License plus experience? I'd imagine it would help.

Nah, without experience the license is no big deal. Won't hurt, but has low likelihood of helping.

While EMT training will provide you an insight into the world of prehospital care that nurses are rarely, if ever, exposed to during their schooling, I ask you this: what advantage for what type of nursing do you expect to get from also being an EMT? If you're looking for something like ED or transport nursing, then perhaps just having the EMT cert might give you an edge over someone that's got equivalent experience as a nurse that you do. The nurse that actually had experience as an EMT would have a significant edge over you, assuming one of the three of you will be hired there.

Bottom line is this: if you go for EMT, do the training and actually work for a while as one. If you're already in a BSN program, you won't have the time to become a Paramedic. Those programs will simply take too long. Furthermore, once you are an RN and have EMT training, some states allow you to challenge the Paramedic exam. You may have to get a certain number of specified patient contacts and/or minimum number of internship hours, but there's often a pathway to that end.

Think about your career goals and how EMT fits into that and you'll have your answer as to whether or not it makes sense.

The other thing to remember is that EMT/Paramedic is not on the same continuum as CNA/LPN/RN. You won't be increasing your nursing skills (and no, I am not talking about manipulative things here) taking a non-nursing course.

If you are turned on by the idea of "doing the stuff EMS does," then go do EMS. If you're going to be an ER nurse, be an ER nurse-- you'll "get to do" plenty of exciting "stuff" there, and learn to do it from a nursing perspective.