Can I use my Apple Watch Series 3 with an international SIM card while traveling in Ireland?

About international roaming

• Cellular roaming isn't supported outside your carrier network coverage area.
• To cover the LTE and UMTS bands used around the world, Apple Watch Series 3 (GPS + Cellular) comes in three regional models – Americas, China, and Europe/Asia Pacific. Unlike iPhone, there isn't a worldwide Apple Watch Series 3 model that supports all cellular bands used globally, so it isn't possible for Apple Watch to roam.
• When your Apple Watch is connected to your iPhone or a previously joined Wi-Fi network, you can still use all the features of your Apple Watch, even if cellular isn't available.

The Apple Watch does not use a physical sim card, it uses a digital one built into the watch and is not removable.

So even if you wanted to, there is no where to place a sim card in the watch.

If the watch is a cellular model, then it will not connect to cell service when out of range of the iPhone, but will still receive messages and calls from the iPhone while in range or connected to the same Wifi network.

If the Watch is the GPS only model, then the sim card inserted in the iPhone is irrelevant to it.

Note that an irish sim card will have an irish number, and all calls and messages to your original number will not be received by the iPhone or the paired watch while the iPhone is using the Irish sim card.