Is it possible to download web apps in ArcGIS Online or Portal for ArcGIS to be used offline?

It is not possible to download ArcGIS Online or Portal for ArcGIS web apps for offline use. This is because web apps in ArcGIS Online or Portal for ArcGIS do not have offline capabilities and are designed to be used through a web browser. A workaround to build offline applications is to utilize ArcGIS Maps SDK for .NET.

ArcGIS Maps SDK for .NET provides a set of software development kits (SDKs) allowing developers to build custom, cross-platform applications for desktop, mobile, and embedded devices. These SDKs also enable offline capabilities, allowing applications to work without a constant internet connection. Refer to Mapping APIs and location services: How to build offline applications for more information.