Are divide and conquer searches applicable to unimodal decision problems?
No.  Any algorithm for this problem requires at least $n-2$ time in the worst case.  Thus, the problem requires $\Omega(n)$ time.  You can't use binary search.

There's a simple adversary argument: each time the algorithm reads some index in the array, the adversary just answers 0.  After the algorithm has read $n-2$ different positions in the array, there are still two possibilities for where the 1 could be, so whatever the algorithm outputs at that point is wrong for at least one input (there exists an input array that makes the algorithm wrong).