This is correct. This will not fix your issue on a high traffic site.
If Apache has, say, a maximum of 50 children and MySQL permits, say, a maximu of 25 connections, then only 1/2 of the children will be able to have a connection to the database.
On a low traffic site, though, as soon as the connection is closed, another Apache child process can make a connection, making it much more likely that a connection will be successful. I've had quite a lot of luck using this method on low to medium traffic sites.
On a high traffic site, it is likely that most of the Apache child processes will be attempting to connect or are already connected at any given time. This is when you should definitely increase the max connections for MySQL.
-Rich