I’m not sure about Verizon, but with AT&T no plans exist they simply bill $2.04 per megabyte of data and $2.00 per minute for calls for the Apple Watch on International Roaming in Europe. You only get to find this out when you get an email saying your watch has reached $100 of roaming charges (about 50 megabytes) and only after calling AT&T because the email doesn’t seem to make sense.
As far as the direct issue here, the same model phones can be potentially different, even with the same carrier. So I assume this is possible with Apple Watches, I would make sure this is not also something Verizon can turn on.
Certainly with AT&T, I do not recommend turning cellular on at all while traveling internationally, unless you want to pay a huge sum since only per megabyte billing is available from AT&T at this point. I will be hopefully be finding a carrier that offers International roaming plans for the Apple Watch. Currently, AT&T does not offer any international Roaming plans for the Apple Watch only per minute/megabyte/SMS message billing.