Well, I had a chat session with an Apple technician and she referred to the Apple Watch guide. The answer is YES. You need to have both wifi and Bluetooth on if you want full connectivity with the Watch. I knew there was some connectivity without this:
Your Apple Watch uses Wi-Fi and Bluetooth to communicate with your
paired iPhone, switching between connections as needed:
- Your Apple Watch uses Bluetooth when your iPhone is near, which conserves power.
- If Bluetooth isn’t available, Apple Watch will try to use Wi-Fi. For example, if compatible Wi-Fi is available and your iPhone isn't in Bluetooth range, Apple Watch uses Wi-Fi.
To enjoy every feature on your Apple Watch, you'll need to enable Wi-Fi and Bluetooth on your
paired iPhone. Swipe up on your iPhone to open Control Center. Make sure Wi-Fi and Bluetooth are turned on.