Hi Simon,
If I understand you correctly, you;d like to add QSpatial as a connection in Map/Pro/Portal? QSpatial is a custom ASP.NET search engine, not an Esri ArcGIS/Portal server. There are however services that are referenced by this search engine. If you click the Search panel on the home, page, then in the search terms section limit the search by Content Type = Service, you'll get a list of search results that include the REST endpoint URL.
Hope this helps
John