Exception handling with std::exception_ptr in OpenMP without locks

I need to include exception handling into OpenMP and already found Elegant exceptionhandling in OpenMP where this code was suggested:

class ThreadException {
    std::exception_ptr Ptr;
    std::mutex         Lock;
public:
    ThreadException(): Ptr(nullptr) {}
    ~ThreadException(){ this->Rethrow(); }  
    void Rethrow(){
        if(this->Ptr) std::rethrow_exception(this->Ptr);
    }
    void CaptureException() { 
        std::unique_lock<std::mutex> guard(this->Lock);
        this->Ptr = std::current_exception(); 
    }   
};
//...
ThreadException except;
#pragma omp parallel
{
    try {
      //some possibly throwing code
    } 
    catch(...) { except.CaptureException(); }
}

My question: Is the lock really necessary?

As far as I understand exception_ptr behaves like shared_ptr, which in turn has the thread safty of a raw pointer. So, multiple simultaneous writes are ok.

And if multiple exceptions from different threads come up, I do not care which one ends up in Ptr as long as one does.

Notes: As already pointed out it is not a good idea to do the rethrow in the destructor. I would have asked my question in the comments there, but I don't have the reputation for that.