No, it is not possible to use the Measurement tools capability in the ArcGIS Instant Apps Basic template as it is not included in the toolset. This is by design. The limited set of tools available in the Basic template is intended for the template to be up and running quickly. Therefore, the ability to measure distance and area and convert coordinates is not included in the Instant Apps Basic template. For further information, refer to ArcGIS Blog: Introducing the Basic template.
As an alternative, use another template with the same capability. These Instant Apps templates include the 3D Viewer, Atlas, Exhibit, Media Map, Nearby, Public Notification, and Sidebar. For further information on app template options, refer to ArcGIS Instant Apps: Choose an app template. Another option is to migrate to another web app with similar tools as the Measurement tools capability. These web apps include ArcGIS Web AppBuilder with the Measurement widget configured, or ArcGIS Experience Builder with the Map widget configured.