Determine whether or not there exist two elements in Set S whose sum is exactly x – correct solution?

Your solution seems fine. Yes you need to sort because its a pre requisite for binary search. You can make a slight modification to your logic as follows:

public static boolean test(int[] a, int val) 
{
    Arrays.sort(a);

    int i = 0;            // index of first element.
    int j = a.length - 1; // index of last element. 

    while(i<j)
    {
        // check if the sum of elements at index i and j equals val, if yes we are done.
        if(a[i]+a[j] == val)
            return true;
        // else if sum if more than val, decrease the sum.
        else if(a[i]+a[j] > val)
            j--;
        // else if sum is less than val, increase the sum.
        else
            i++;
    }
    // failed to find any such pair..return false. 
    return false;
}