Hi,
The reason that hosting companies encourage you to close connections is that only a limited number of sockets connections can be opened on any server (be it windows or linux)
On a shared server this can be used up pretty quickly.
The connection opening in fact has some overheads. So on well managed connection pooling systems (not talking just of PHP here) when you attempt to close the connection what really happens is that the connection is returned to a pool. It's kept there for a few minutes in the hope that someone will claim it. After that it's closed automatically.
well this is atleat my understanding of matters :-))