Yes, there is a standard SAP transaction called WDYID that can open a Web Dynpro ABAP application within the SAPGUI or in a new browser session. You won't be prompted to login to the application again because the SAPGUI will generate a SSO Ticket off of your SAPGUI login.
You can create a parameter transaction for WDYID and supply a value for the screen field APPLICATION (the WDA you actually want to run). You can check the Skip initial screen value to directly launch the WDA. If you have a late enough SP level, have a look at the SOAMANAGER transaction code as an example of how to do this.
You can also directly link a Web Dynpro ABAP application into a PFCG role. It will appear on the main menu of the SAPGUI and launch using the same mechanisms as the WDYID transaction code.
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