I don't think that's possible since a gadget is also an application and you can't run an application inside an application. I got this error message when trying:
Warning: Error in shiny::runApp: Can't callrunApp()from withinrunApp(). If your application code containsrunApp(), please remove it.
ps you can change the viewer argument of runGadget, so it opens in a dialog or browser, just like a shiny app