Getting a PHP PDO connection from a mysql_connect()?

I have a legacy PHP/MySQL app that calls mysql_connect(). Tons of existing downstream code makes mysql_query() calls, either directly or through wrappers, using this connection.

For new code that I develop on the app, I would like to start using PDO.

If I make a PDO connection using the same host/user/pass/dbname credentials, might I be so lucky that under the hood, PHP will re-use the original connection? Or will PHP create two distinct connections to the server (undesirable, albeit totally understandable)?

Thanks!