Does the Predator drone's design make a tail strike more likely on takeoff and landing?
The tail arrangement was initially chosen to protect the propeller from touching the ground first. The configuration of what later became the Predator was initially designed to be launched from a submarine, so it needed to fit into a torpedo tube when folded. When this configuration was scaled up, the general arrangement was kept. Now the tail surfaces are much larger relative to the propeller, so the initial reason for their location is not easily discernible.

The high aspect ratio $AR$ of the Predator's unswept wing gives it a much higher lift curve slope than that of the swept wing of an airliner, so less rotation is needed to increase lift for take-off. Also, the highly cambered airfoil has a very low, negative zero-lift angle of attack, so at level attitude the wing already produces substantial lift. This was chosen to fly at optimum endurance speed with a horizontal fuselage attitude. The lift coefficient $c_L$ for optimum endurance is $$c_L = \sqrt{3\cdot\pi\cdot AR\cdot\epsilon\cdot c_{D0}}$$
At that lift coefficient, induced drag $c_{Di} = \frac{c_L^2}{\pi\cdot AR\cdot\epsilon}$ is three times bigger than zero-lift drag $c_{D0}$, which means endurance is longest when the aircraft flies at a high lift coefficient and low speed. Basically, the Predator is a point design, flying almost always at the same attitude and lift coefficient. Ground attitude equals flight attitude, and a rotation beyond a few degrees will make it stall.