Is the compiler allowed to reorder statements around `std::condition_variable::notify_one`?

Question

The following code is a struct I have written to allow me to queue up work to run on multiple worker threads, and which blocks the main thread until a new worker thread is available.

struct WorkQueue{
    const std::size_t size;
    std::vector<uint8_t> threadActive;
    std::condition_variable cond;
    std::mutex mu;

    std::vector<std::jthread> threads;

    WorkQueue(std::size_t size_ = 1) :
        size{size_}
    {
        threads.resize(size);
        threadActive.resize(size);
        std::fill(std::begin(threadActive), std::end(threadActive), false);
    }

    template<typename Function>
    void enqueue(Function&& f){
        auto numActiveThreads = [&](){
            return std::count(std::begin(threadActive), std::end(threadActive), true);
        };
        auto availableThread = [&](){
            return std::find(std::begin(threadActive), std::end(threadActive), false) - std::begin(threadActive);
        };

        std::unique_lock<std::mutex> lock{mu};

        //wait until a thread becomes available
        if(numActiveThreads() == size){
            cond.wait(lock, [&](){ return numActiveThreads() != size; });
        }

        //get an available thread and mark it as active
        auto index = availableThread();
        threadActive[index] = true;

        //start the new thread and swap it into place
        std::jthread thread{[this, index, fn = std::forward<Function>(f)](){
            fn();
            threadActive[index] = false;
            cond.notify_one();
        }};
        threads[index].swap(thread);
    }
};

I have two questions about the code in the lambda executed by the jthread:

1. Is it necessary to lock the mutex mu when setting threadActive[index] = false?

2. Is the compiler allowed to reorder the code and execute cond.notify_one() before setting threadActive[index] = false?

I think it is necessary to lock the mutex if and only if the compiler is allowed to reorder the statements. Is this correct?