You are correct. There are a lot of good articles explaining ADO connection pooling. For exmaple, MSDN - SQL Server Connection Pooling (ADO.NET), which says:
Connection pooling reduces the number
of times that new connections must be
opened. The pooler maintains ownership
of the physical connection. It manages
connections by keeping alive a set of
active connections for each given
connection configuration. Whenever a
user calls Open on a connection, the
pooler looks for an available
connection in the pool. If a pooled
connection is available, it returns it
to the caller instead of opening a new
connection. When the application calls
Close on the connection, the pooler
returns it to the pooled set of active
connections instead of closing it.
Once the connection is returned to the
pool, it is ready to be reused on the
next Open call.