From my non-scientific analysis, I would say there are definitely problems with having an Apple Watch connected when using Airpods, especially when it comes to Siri. Add a BT connection as well into the mix, and things go downhill even further.
As mentioned, activating Siri from either Airpods with a double-tap does indeed activate Siri but then Siri not hearing anything or reacting to any voice input whatsoever happens more than I would like. It does seem, more often than not, putting the Apple Watch into Airplane mode puts things right again with full activation and Siri response.
Overall I would think this is an iOS specific issue with the BT stack and customizations made to support the W1. I think Apple is aware of this because when I exchanged my last pair (due to incoming call voice problems), there were specific questions asked by the genius that included the overall use-case and Apple Watch use were part of the questions.