Yes, it is possible to send a message on WhatsApp without adding the contact to your phone's address book. Here's how you can do it:

Open NoSave App

In the box that appears, enter the phone number of the person you want to message, including their country code (e.g., +1 for the United States).
Click on the person's name or phone number when it appears in the search results.
You can now send messages to the person without adding them to your phone's address book.
It's important to note that the person will be able to see your phone number if you message them in this way, so make sure you are comfortable with sharing your number with them.