I would have never thought so, but Amazon's own data has shown that seemingly trivial things like increasing page load times by 100 ms reduces sales by a non-negligible %.
We're all arguing over data we don't have, but if they have that kind of information I think they have also considered search box focus. Seeing that they don't have it, one can draw the conclusion that for their site it was not profitable.
Why do you think they obsess over dropdown menus?