I think taking a doula training before you become a nurse is a very good idea. That's actually what I have done. I feel it will make me a better nurse in the future because right now I am learning how to support women emotionally and physically.
I have had a baby, but only 1 out of my 6 clients has expressed their discomfort with having a doula that hasn't had a baby. Honestly, the only advantage that you would have if you had a baby is being able to bring examples of your personal experience when talking to the client prenatally.. and I know some doulas who just talk about their births, that happened to them, how they felt NONSTOP and it really annoys the client. They need to remember they are there for HER!
At the doula training I went to, there were 20 women. 5 of them were nurses and 3 of them were in nursing school. The nurses said the doula training was very helpful to them, because not only do they learn the role of the doula and better understand how to work with one, but they learn how the doula supports the mother emotionally and may be able to do the same.
I do think it is unrealistic to try and be a doula during full-time nursing school unless you are willing to miss a day or two of classes. You never know when a client will go into labour and it might be 6am the morning of a day you have classes and she could labour (hopefully not) until the next day. You just have to weigh the pros and cons I guess.
But I think the course is a good thing to take just for the information if anything. Good luck