Yes, you have to create the index in Word before you convert the file to PDF.
What you can do is create the three files (book part 1, book part 2 and index) as PDF files from Word, and then use the File>Create>Combine Files into a single PDF optioin in Acrobat to combine the files into one PDF file.
You may be able to select your three Word document in this operation, and have Acrobat convert the files to PDF before combining them.