Hi
GPS-only models
If you are asking about an Apple Watch Series 3 (GPS) model, then yes. Apple Watch Series 3 (GPS) models can be used for calls and texts on any cellular network that your iPhone is using, subject to connection requirements.
The full range of features is available when Apple Watch and iPhone are connected via Bluetooth and your iPhone has access to both cellular service and the Internet (via either cellular data or Wi-Fi).
You don't necessarily need to have your iPhone on or immediately around you (within arm's reach, for example) for the devices to establish and maintain their Bluetooth connection. Normal Bluetooth range is around 33 feet / 10 meters (this will vary in practice due to wireless interference).
Whenever your watch can't connect to the iPhone via Bluetooth, it will attempt, as a fallback, to connect to a known Wi-Fi network - this being a compatible 2.4GHz Wi-Fi network (some exceptions apply) that your iPhone has connected to before whilst your Apple Watch was connected to the iPhone via Bluetooth.
When instead connected to Wi-Fi, the watch also still offers a number of features, including receiving and sending messages via iMessage. If your carrier offers Wi-Fi Calling and it is supported on your plan and enabled on your iPhone, you can also use Apple Watch to make calls and (subject to carrier support) to send and receive SMS / text messages.
If your Apple Watch is unable to connect either via Bluetooth or Wi-Fi, it again still offers some - although fewer - features.
Features that are available in each case are detailed here:
How to use your Apple Watch without your iPhone nearby - Apple Support
For the best performance from your iPhone and Apple Watch, including the most power-efficient communication between them, Apple recommends keeping both Bluetooth and Wi-Fi permanently enabled on your iPhone.
More information:
Apple Watch (GPS + Cellular) models
To be able to Apple Watch (GPS + Cellular) models for cellular features when it is not connected to either the paired iPhone or trusted known Wi-Fi network, you would need a carrier plan that specifically includes support for Apple Watch, including the carrier activating the device on the plan.
If your carrier does not offer a suitable plan, then you cannot currently use the built-in cellular feature. However, Apple Watch Series 3 (GPS + Cellular) can still be paired, set up and used for other features after skipping the steps to activate cellular (acting like a GPS model). The cellular feature can be enabled later, if and when you have a compatible service plan.
More information: