If I understand your question, it is basically an identification when a PDF is downloaded completely in the browser. As long as you can identify the start of PDF download and the end of PDF download, you can use the Dynatrace RUM API to capture the action. - dtrum.enterAction() and dtrum.leaveAction(). Then the PDF download would be a separate custom action. Alternatively, if you want to include it in the XHR/Load user action, you can use dtrum.setLoadEndManually() and dtrum.signalLoadEnd().
One possible approach is to set a cookie with the downloaded PDF and check in the application if the cookie is already present. This would indicate a finished download.
Anyway, you will need to modify your application to capture this information and send appropriate events.