In these senarios I want to test two things
Do my tests pass for each individual server
Do my tests pass for the load balanced endpoint
In order to test individual servers I need to be able to address them directly. This can be done by going direct to each box, or by providing a routing parameter to the LB which bypasses the nomal host selection.
I can ...
Purists won't call any test a "unit test" which involves a database. Other purists won't call a test an "integration test" when there are not at least two components involved (and a platform like the SQL engine of the DB usually does not count as a component).
And some not so puristic people call everything a unit test which gets started by an automatic ...