Right now Special:JavaScriptTest/qunit/plain exports page-specific mw.config values provided by OutputPage (in addition to the site-wide values from the startup module).
There's only a few random tests here and there that accidentally depend on mw.config values (usually whatever the default is). This should be resolved by setting the relevant values in the test suite from a setup handler.
There are also some cases where a module both exports an interface (which is tested) and self-initialising code for a wiki page. In such case, the initialising code usually runs immediately and thus before the test start. While having that run as a no-op is fine. Issues arise from values missing in mw.config as init code rightfully requires those values to be present in mw.config.
In those cases, the initialisation code should be run from a hook like wikipage.content (which doesn't run in the test suite). Or moved to a separate module not loaded by the test. Or, if the init code is testable, it should additionally be exposed so that its execution can be controlled by the test instead of at runtime.