With white box testing, you know exactly the internal implementation of your application. Tests are designed so that each path (or line of code) is executed at least once. It is usually employed to test applications where the expected level of reliability is high or when the safety of an individual is involved.
With grey box testing, you don't know the implementation, but you know the design or the data flow from the documentation which seems to be the case here.
So no, the test you are describing doesn't fall under white box testing and grey box testing would fit better.
Note that this test is an integration test and not an end to end test. Moreover, using a query provided by the developer kind of defeats the purpose of the test since the query you are getting is probably used by the application itself. So if it's defective (double records, different casing, improper encoding...), it will then make your test irrelevant.