Could I upgrade my existing SAP solution (for example, R/3 4.5) to the SAP Web Application Server 6.20?
No, this is not possible and was also not possible for previous SAP solutions. Then, the SAP Basis (which is now SAP Web Application Server) was in a composite with the application component. That bundle was shipped as a SAP Solution like R/3 4.5. The upgrade was always an upgrade of the whole bundle. This means that to use the SAP Web Application Server features you have to install a SAP Web Application Server separately in front of your existing SAP System and connect to that system using RFC, for example. Or you have to upgrade to the SAP solution, which is based on the SAP Web Application Server like R/3 Enterprise.