No. The app is not required to use the scale. The scale can function on its own, including mode changes and tare.
To change the units to grams/ounces on the Acaia original Pearl firmware 2.0, hold town the tare button when the scale is in weigh-only mode. When you change the unit into oz there will be a small green LED indicates that it is in oz mode. There is another small orange LED that will indicate charging. These LEDs are hidden when not lit.
To change the units on the Acaia Lunar, you can either use the Acaia Coffee app or switch it through the scale's settings menu. The app can be found in Apple's App Store or in the Google Play Store for Android devices.
For the Pearl Model S there are a number of features you will miss out on without the Brewguide app, but will still be functional.