Patch the db conn pool sooner in tests (#17017)

When running unit tests, we patch the database connection pool so that
it runs queries "synchronously". This is ok, except that if any queries
are launched before we do the patching, those queries get left in limbo
and never complete.

To fix this, let's change the way we do the switcheroo, by patching out
the method which creates the connection pool in the first place.