Depends ..
If you work with MySQL, keep in mind that MySQL by default only supports 100 connections at same time, if you want to use persistent connections and your site have a lot of traffic, you should increment this number (I think 1024 its the max. value).
If you have the mysql in the same server where there is your http server, I would not use persistent connections. Otherwise, yes, except if the site have too many connections that could cause problems to MySQL.
To destroy the object, I think isn't needed, PHP clears all that from memory after the execution, and usualy, the live of a PHP execution is very short (for web scripting).