No, you are free to save it there, but I don't see the real benefit since technically any device that can access the Passwords App is already signed in to your Apple Account, and if a device is not signed, then you don't have access to passwords app anyway to see the password there.
The only reason I see to have it there, is to be able to log in to your Apple Account on the Apple account website, or iCloud.com or some other Apple website that requires it more easily. The first time you do that, you'll be asked if you want to add it to the Passwords app.