Does Straight Talk work with an Apple Watch?

Apparently not:

Apple Watch - Carriers - Apple

If you always have your iPhone nearby, then you can use a GPS only Apple Watch, and it will do EVERYTHING an cellular model will do AS LONG AS your iPhone is nearby, so the Apple Watch can use the iPhone's radios via low energy Bluetooth between the 2 devices.

A GPS only Apple Watch does not care about the iPhone's cellular provider, and the cellular provider does not know you are using an Apple Watch.

A cellular Apple Watch can leave the iPhone at home when you go for a walk, run, bike ride, etc... and still make/receive phone calls, send/receive messages, etc...

The GPS only without the iPhone will still track your exercise and sync the information back to your iPhone Health app when you get back home.