Yes: the entire what3words’ system is very compact, and so it can work offline when you don't have a data connection - you only need a GPS signal. Often your phone will still have a GPS signal even when you don't have network reception, or a data (internet) connection. The map on the screen may not load with a GPS signal alone, but if you press the 'current location' button your 3 word address should update.
The what3words app is designed to be used offline with compass mode. Compass mode is one of the navigation options in the app - it will show the direction you need to travel, and the distance to your destination, but no map so no turn-by-turn directions. Full offline maps and directions are available in some of our partner apps, such as Navmii.