I'm not yet sure which operators perls overloading can handle
AFAIK All of them. Even the handling of different quoting types in the code.
Its a fallback system however. If the operator is explicitly defined then that definition is used, otherwise if overload can syntheisze the behaviour of the opertor in question by using a different defined operator then it will do so. For instance defining '<=>' and 'cmp' with the normal settings (the fallback behaviour is configurable) iirc will cause all of the equivelency operators, numeric and string, behavior to be overriden.
One thing you have to watch out for however is the common debugging habit of stringifying references by concatenation. The "" operator can cause some suprising results.
A fairly common use of overload might be
When the right hand side is a string as it is in this case then the handler is expected to be a method of that name called against the object. Otherwise a coderef is expected.
The overload docs were written by a mathematician which is why they are relatively incomprehensible to mere mortals like us. Its incredibly easy to miss details or become confused when reading that document. I think I've read it at least ten times and I still find things I haven't seen before.