If all you want to do is to write, then I would suggest educating yourself in a far less expensive manner than a naturopathic program. All you really need to write a book is a target audience and a good knowledge of the subject material. I would also suggest that you will need to be very familiar with searching and interpreting research from various medical databases such as Medline.
One much cheaper option than naturopathic school would be to get a Masters in Nutrition. University of Bridgeport has a really solid, accredited, program with an online option. The program can be done in only 2 years and you can still work a normal job. By the time you are finished, you will know how to work with patients on their nutrition, how to read the literature, and apply nutrition to real people. They also have a project that they make you do which would be a very good bridge towards writing a book.
Remember-- no school will give you the knowledge you need to write a book. They willl only provide a framework towards helping you be able to self-teach yourself and compile the material you need to write a book. Many of the courses taught in naturopathic school would be a waste of your time. There is a lot of fluff classes in this degree.
Many people are writing books these days that have no more than a little education and a thing like a personal trainer license. It doesn't take much. E-books have also become increasingly more common.
http://www.bridgeport.edu/pages/3246.asp