Answer
The rope cannot be made to be perfectly horizontal.
Work Step by Step
The figure below shows the forces acting on the crate. As you can see, having the rope not horizontal means the tension forces $T_l$ and $T_r$ having vertical components $(T_lsin\theta$ and $T_r\sin\theta)$, which point upward.
These vertical components are essential to the equilibrium of the crate because they balance the downward gravity force $mg$ on the crate.
Therefore, if the rope is completely horizontal, $T_l$ and $T_r$ will not have vertical components, and since there is only 1 vertical force downward, the crate will always have vertical acceleration and never will be in equilibrium.
