"Is a service book necessary?" It depends what you define as necessary. Will the lack of a service book affect a warranty claim? Subject to associated paperwork, no. Could a future sale be affected if I don't have the book? Potentially, there are enough buyers out there who insist on seeing a "stamp" in a book.
For the sake of a phone call to the salesman, I highly recommend. To a dealer, a service book missing is not uncommon so it is not unusal for a dealer to acquire a replacement service book, send off to the relevant dealerships and get the stamps in the book, it is a more than fair request and from my experience of these issues, never had a problem with getting dealers to do this.