The point of optional, gradual typing is to offer optional type safety.
This seems like a tricky feature in an allomorphic language like Perl, where intrinsics are polymorphic and operators are monomorphic.
I would suggest that any non-overloaded reference would also throw an exception.
I think there are cases where default stringification is desirable, and I suspect you'd have to go through each operator and each intrinsic to come up with a matrix of where it might be useful. This seems like a similar problem to smart match (though less so, because stringification for types should be a unary op, not a binary op).