Exercise 2.3.6

Observe that the while loop line 5-7 of the INSERTION-SORT procedure in Section 2.1 uses a linear search to scan (backward) through the sorted subarray $A[i..j-1]$. Can we use a binary search (see Exercise 2.3-5) instead to improve the overall worst-case running time of insertion sort to $\Theta(n\lg{n})$?

No. Even if it finds the position in logarithmic time, it still needs to shift all elements after it to the right, which is linear in the worst case. It will perform the same number of swaps, although it would reduce the number of comparisons.