When running arimidex, I believe the test wouldn't become less effective, it should become MORE effective. The reason why is without a-dex, a percentage of your free testosterone is converted to estrogen (a fixed percentage regardless of how much test is in your system). A-dex prevents aromatization, which means virtually no test is converted to estrogen. The result should be higher testosterone levels.
When running a-dex, the test may FEEL less effective because you are not getting the bulking benefits (some would not consider them benefits) of estrogen. But I do believe while on a-dex, blood levels of test should be higher than without a-dex.