The efficiency benefit provided by the persistent connections, specifically in establishing the connection, will be enormous if you actually have 10k processes querying the database.
Assuming you're running PHP under Apache, the first time a SQL connection is made the Apache "child process" will keep it open (i.e. - the persistent connection). All PHP requests that belong to that specific "Apache child process" will reuse that connection, if the connection information is the same of course. Apache's configuration defines how many requests a single child-process can handle before it is restarted - which should clear the persistent connection.
Now, there is also the case that you are running queries in a loop or even - dare I say it, an infinite loop. In that case, even a non-persistent connection would be deadly.
It is doubtful that the number of processes using your persistent connections will be a factor in the server's efficiency (unless, as I mentioned, you have some in-efficient code using queries). The thing that should be focused on is how many persistent connections should you allow and how many can your database/server handle?
The MySQL manual for the persistent connections, http://php.net/manual/en/features.persistent-connections.php, also covers most of (and more) of what I just summarized.