I really doubt there's any data size for which sort + binary search is going to be faster than linear search. The former has higher complexity (so it's going to be slower for large inputs) and more expensive operations (so it will be slower for small inputs).
You can also think about it as a sort of reductio ad absurdum: Assume that the array is actually already sorted and you use a sorting algorithm with O(n) complexity for already sorted data. In this ideal case you'd need to do n (for sorting) + log n (binary search) predictable operations. For linear search you'd only need to n operations of the same type. In practice you'd need to do n log n operations for sorting, I don't think you can avoid unpredictable branches, and instead of just loading elements sometimes you'll move them around.
You can also think about it as a sort of reductio ad absurdum: Assume that the array is actually already sorted and you use a sorting algorithm with O(n) complexity for already sorted data. In this ideal case you'd need to do n (for sorting) + log n (binary search) predictable operations. For linear search you'd only need to n operations of the same type. In practice you'd need to do n log n operations for sorting, I don't think you can avoid unpredictable branches, and instead of just loading elements sometimes you'll move them around.