Hi! I'm currently on my last semester in nursing school while doing Navy ROTC. There are definitely pros and cons about joining ROTC while in school but I think the best thing is that you have a lot of peace of mind when you have a job lined up after you graduate. All my friends are frantically trying to find jobs/create resumes/etc but I'm just chilling, especially after I found out about my first duty station! I think it's true what jfratian said about how the first one or two years will be helpful if you are in ROTC, but doing DA wouldn't harm you in any way.
While doing ROTC, I was able to do Summer training opportunities in a ship and the San Diego Balboa hospital so I have more knowledge than the Nurse Candidate students that I met online but I believe that once everyone gets there (as a nurse and starts working), it evens out.
To be honest I definitely don't do that many extracurriculars because ROTC keeps me busy (as well as nursing) but I don't feel like I am missing out because I am able to do clubs that I want to do and my closest friends are my ROTC friends. There are many events that I actually get out of because of nursing (like clinical schedules, etc).
Overall, I 100% support doing ROTC, but your situation might differ. I don't believe Navy ROTC does any 3- or 2- year scholarships (as they keep saying that they are getting rid of the program and I only have 10 other people in my graduating cohort), but I think any branch ROTC is great! I have 3 friends who did Army ROTC nursing and one is at Bethesda and one is at Fort Belvoir. I know a girl in Air Force ROTC but I haven't been able to really ask what she does in terms of training but I'm biased to Navy :)
I hope this somewhat helps!