No, the rewritten URL is an internal mapping process only. It is only used by your web server to determine how to treat the user-friendly URL it receives.
The same way the URL remains unchanged in a browser address bar, the process is invisible to the client, be it a web browser or a bot.
URL Rewriting is not to be confused with Redirection. In the latter case, a client request receives a "301 Redirect" response containing the URL where the actual resource resides. This results in a second request from the client to the redirected URL. Then by definition the client will be aware of this process.