If I bring the Apple Watch to Chile, will the cellular work?

That depends on the model and where it was purchased.

Series 8, Ultra I or older, have region specific cellular radios. The Canada, U.S., Mexico, Puerto Rico region. And the rest of the world region. These radios will not work outside their region, except for India, which seems to accept all Apple Watches.

The Series 9 and Ultra II seem to have just one cellular radio, so should be able to work with any carrier.

Finally roaming. Do you want to transfer your iPhone and Apple Watch to a carrier cellular plan in Chile, or keep your current carrier plan and depend on cellular roaming?

Set up cellular on Apple Watch - Apple Support

scroll down about 3/4 of the way and they talk about roaming (IF AND ONLY IF, your cellular radio chip supports the region you are roaming in).

it depends on if the carrier you have tied to the watch has a roaming agreement with carriers in chile

you can up on what roaming means if you do not know going here Roaming - Wikipedia

mind you when roaming calls, sms and MB data prices can be wastly higher then when you are in your own country