Yes, it is possible to generate a short URL for ArcGIS Web AppBuilder using the Share widget. Generated short URLs contain all the parameters listed in the original URL.
Follow the steps described to add a Share widget in ArcGIS Web AppBuilder to generate a short URL.
Note: Creating an ArcGIS Web AppBuilder app from a web map is not supported in Map Viewer. Refer to ArcGIS Online: Create apps from maps for more information.
Note: Different map extents and zoom levels generate different URLs. Despite these settings, all generated URLs redirect to the same web application.