Seres 8 and older come in 2 different models that have different cellular chips. The Canada, U.S., Mexico, Puerto Rico model, and a model for the rest of the world.
So a U.S. model will not connect to cellular in Europe.
The Series 9 Apple Watch does not appear to have different models for the Americas vs the rest of the world, except China and Hong Kong.
If we are talking the Series 9, then maybe it can work, but we have no real world evidence yet.
Apple Watch uses the iPhone’s phone number.
If you change your iPhone’s SIM (or eSIM) to a different carrier, you would have to contact with that carrier to allow your Apple Watch to share that new number. That would eliminate the inexpensive short period of time eSIM vendors often used for vacation travel.
The most likely thing is to get an inexpensive vacation eSIM for your iPhone, and let the Apple Watch revert to GPS only mode while on vacation, allowing the Apple Watch to use the iPhone’s radios for phone calls when the 2 are nearby.