Sometimes it should, especially when testing the overloaded objects. It is the lack of any is_deeply test which is able to see through overloading that lead me to do something hokey and do cmp_eq( Data::Dump::Streamer::Dump($a), 'eq', Data::Dump::Streamer::Dump($b) ) tests instead.
If an overloaded object wanted to pretend to be normal, it can use an utterly normal test and it'll get called as usual. Its the stuff like Test::More which should be able to have x-ray eyes to see through overloading.
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