Is it worth applying asynchrony for summing elements of a large array containing a billion numbers?

Yes, applying asynchronous techniques to sum the elements of a large array of a billion numbers is justified. Such a task is well parallelizable because addition is an associative operation.

You can split the array into several parts and compute the sum of each part in parallel, using, for example, Task or Parallel.For in C#:

using System;
using System.Threading.Tasks;

class Program
{
    static void Main()
    {
        long[] largeArray = new long[1_000_000_000];
        // Array initialization...

        int processorCount = Environment.ProcessorCount;
        long[] partialSums = new long[processorCount];

        Parallel.For(0, processorCount, i =>
        {
            int start = i * largeArray.Length / processorCount;
            int end = (i + 1) * largeArray.Length / processorCount;
            long sum = 0;
            for (int j = start; j < end; j++)
                sum += largeArray[j];
            partialSums[i] = sum;
        });

        long totalSum = 0;
        foreach (var sum in partialSums)
            totalSum += sum;

        Console.WriteLine($"Total sum: {totalSum}");
    }
}

This approach significantly speeds up the computation by utilizing all available CPU cores.