Can be totally different if you use some connection pooler like pgpool or pgbouncer - these applications can reuse Postgres server sessions for more user sessions.
BTW, AFAIK, it's not possible to change the session authentication information by
using SET SESSION AUTHORIZATION [1] if the current user is not a superuser.
But it would be very nice to have a feature to change the session authorization
of current user even without superuser's privilege by supplying a password of
the user specified in SET SESSION AUTHORIZATION. This feature allows
to use PostgreSQL's native privileges via connection pools -- i.e. without
needs to open a dedicated connection for authenticated user. Is it possible