Yes.
I do this all the time.
For example, when riding my bike, I’ll listen to a podcast or music on my iPhone, via my AirPods. If during the ride I want to message my Wife, I’ll raise my GOS Only Apple Watch arm an say “Hey Siri, message [insert Wife’ name here], I just saw the most amazing thing…”
The Apple Watch will be using Bluetooth to get the iPhone to process the Siri request, and and send it via iMessage. All the while my AirPods are playing in my ears.
The iPhone Bluetooth can walk and chew gum at the same time.
NOTE: In the winter I might also take a walk with some Sony over the ear Bluetooth headphones as earmuffs instead of the AirPods, as a way to listen to music or podcasts from my iPhone, while also keeping my ears warm.
And while you did not ask, I will mention, it is possible to pair Bluetooth headphones to the Apple Watch and the Apple Watch can still use Bluetooth to talk to the iPhone. I do not do this, as there is no advantage to me, since I have my iPhone with me and it has a much larger battery vs the Apple Watch.