Samozřejmě, že může
https://en.wikipedia.org/wiki/Operator_overloading
https://en.wikipedia.org/wiki/Operators_in_C_and_C%2B%2B#Assignment_operators
All assignment expressions exist in C and C++ and can be overloaded in C++.
Addition assignment | a += b | R& K::operator +=(S b); | R& operator +=(K& a, S b);