No, this is not possible. Pointer types are scalar types, but overloading operators requires a non-scalar parameter. In particular ([over.oper]p6):
An operator function shall either be a non-static member function or be a non-member function that has
at least one parameter whose type is a class, a reference to a class, an enumeration, or a reference to an
enumeration.
If you had a binary operator where one parameter was a user-defined type and the other a pointer, that would work, but in the situation you're asking about, both operands are pointers.
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