Yes, as explained in the support document you came from:
- When your iPhone asks if you want to use your Apple Watch, tap Continue.
- Follow the onscreen steps to finish setting up your new iPhone and Apple Watch.
- Your Apple Watch will ask for your passcode and confirmation to begin the transfer.
- Open the Apple Watch app on your iPhone to make sure that your watch is paired.
The old watch will then be paired to the new iPhone.
After that, you can then unpair the watch and pair the new new one, or leave the old one paired.
There's no point in setting up the new watch with the old iPhone and then setting up the new iPhone.
Set up the new iPhone, and then pair the new watch to it.
Use more than one Apple Watch with your iPhone - Apple Support