Connection Pool confusion - New Schema = new connection?

Confusion on Connection Pool in relation to Database Instrumentation from Oracle DBA perspective - somehow I'm thinking they should work together to get full benefit of connection pool

Connection pool is useless unless I'm using same schema over and over again?

If I login with different schema name everytime, a new connection will have to be created for that schema in addition to the idle ones (connection pool keeps a minimum number of connections open)?

However, to make connection pool useful I need to use one schema for the whole application. I would create all users under one schema and manage it all using database instrumentation.