Does Apple Watch record data from external HR sensor when off wrist?

Some further findings after 10 days of frequent use and experimenting.

1. Even if you have Wrist Detection off, the Workout app pauses by itself after about 20 seconds. Simply swipe right and tap Resume to keep the app running. It only pauses once. After tapping Resume, the app keeps running, recording the workout until you tap End.
2. Sometimes the built-in optical HR sensor overrides the external HR sensor, even if the external sensor is connected to the watch via Bluetooth. This is the case if the green LED lights at the back of the watch are on when they shouldn't. When this has happened (just once so far), I've simply restarted the watch. After restart, make sure the external HR sensor is connected to the watch. Now, the external HR sensor is the one in control, sending HR data to the Workout app; the green LED lights are off.

Ok, I'm answering to myself. (And I was actually referring to the Workout app of the Apple Watch in my original post; not the Activity app. Sorry about the confusion.)

I couldn't wait, so I went and bought the Polar H10 and started experimenting. I paired the H10 with my Apple Watch using the Settings app on the watch. I didn't use any Polar apps. Nor did I pair the H10 with my iPhone.

Answering the original question: Yes, within Bluetooth range Apple Watch can be off wrist and still be recording the HR data received from the external sensor. But my first tests suggest that this is possible only if the Wrist Detection is turned off.

The Wrist Detection toggle is within the Passcode section of the Watch app on iPhone.

Having the Wrist Detection off seems to affect the Stand hours in Activity app: when the Wrist Detection is off, no standing is detected. There might be also some other side effects, but at this point I'm not worried about those. I guess it's a good rule to have the Wrist Detection off only when I'm not wearing the watch on my wrist but still want to keep the Workout app running. I'll keep experimenting with different settings and options.