[websites222]

If you have the cellular version, yes. However, I have found that the handoff from WiFi to Cellular is terrible. It takes a few minutes for the watch to realize it's not going to reconnect to WiFi soon, and in the meantime you're just sort of left waiting for when it decides to switch over to cellular.

This is especially annoying if you're listening to streaming radio (like NPR) and going for a walk. It will just drop. This has been the case since the very first version of the cellular watch, I suspect as a battery-saving feature.

The only way to really get around this is to force cellular mode before you leave. This is what I do, and it's embarrassingly un-Apple in experience:

(1) Put my iPhone in Airplane mode. I think I could accomplish the same thing just turning off BT, but I want to be really sure the phone and watch are cut off from each other.

(2) Turn WiFi off on my Apple Watch. Wait a few minutes(!) before I go for a walk -- make coffee, leash up my dog, etc

(3) Walk outside, and issue my Siri command to trigger music/radio

This usually works fine. But its annoying. If you're not especially dedicated to going phone-free (it drains the battery quickly) I really wouldn't bother.

[DeRock]

> If you have the cellular version, yes

No, you can use AirPods on a non-cellular watch just fine, it has bluetooth. Cellular only affects your ability to stream content (eg. Music or podcasts), but you are also able to download/cache those while on WiFi on the non-cellular watch.

[websites222]

The OP's definition of "work" went beyond whether the AirPods connected directly to the Apple Watch:

>As in, if I leave my phone at home, will I be able to stream music and calls from my watch to my AirPods while I go for a run?

For my response, I assumed two things:

(1)"Streaming music" meant listening to music that is not stored on the device.

(2) "Calls from my watch to AirPods" meant that during a run, OP was not in constant range of a remembered, open WiFi network.

[bestnameever]

I don't have cellular enabled currently on my watch but I remember it connecting to cellular very quickly.