... has a value of NaN, which is false.

Ok, I'm confused. In your OP, you say NaNs are true. Now you're saying they're false.

Update: I see, you're talking about your overloaded version, which changes the "sign" of NaN. Ok, I agree that changing that is a Bad Idea in general, because of the violation of expectations.

So, I guess you'll be stuck (assuming you ditch your overloaded version) doing an explicit test for NaN...

  if ( $obj == NaN or $obj ) # true if true or NaN
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in which case, you could wrap it in a new method:

  sub isTrue # !
  {
     my $obj = shift;
     $obj == NaN || $obj
  }
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