You can sort of do it so long as the return type is a template parameter.

    template<typename T>
    T my_construct() { T result; return result; }

You certainly can and I know there are several JSON libraries that do it. The gist of it is to write a struct and overload the conversion operator for the set of return types you want to support, for example overload the conversion operator to int and std::string. As soon as the instance of that struct is used in a context that needs an std::string, then it calls the string overload.

You can, if you abuse C++ enough. I needed this very thing for a custom DSL.

    struct PolyReturn {
      const int value;
      operator int() const { return value; }
      operator bool() const { return value > 0; }
    };

https://cppinsights.io/s/f0b9976f