I'm sorry if I was not exactly precise. A more precise statement would have been "If the exception is not caught, then Perl itself prints it out which has the result of stringifying it. Hence it prints "Fart=ARRAY(0x...)", i.e. the default stringification of a blessed object, if you don't overload it and whatever you overloaded it to do otherwise. That's at least what I see on my machine with Debian Linux/Perl 5.10. Do you see something different?
Now, I hope you will not mind if I offer a slight clarification on your words.
When testing an exception, one cannot assume that it will be stringified. That depends on how one does the test, whether or not overload's "fallback" option is used, and what other operators are overloaded with a custom subroutine. For instance, if one tests by doing if (!$@) and you've overloaded !, then the overload for ! will be invoked, not stringification. If instead you do if ($@), then Perl will first look for an overload for "bool". If you have disabled fallback and you do not define the "bool", operator you will get a complaint "Operation 'bool': no method found". Only if you enable fallback, will it stringify the object to compensate for the missing bool operator definition. See overload for further discussion.
Also, just to be clear, in none of these cases (printing, testing) is the object itself destroyed. The application of the !, bool or "" operators are strictly for evaluation in context. The exception object remains an object before and after.