If we had the ability to make an actuator that could turn around at or past the speed of light and I attached a high miliwatt laser to it, then spun the laser around on the actuator at the speed of light, would the light beam bend act like a the stream of water from a spinning hose as the laser went around it?
Yes the light beam behaves exactly like the water. In both cases particles are emitted in a specific direction and travel in a straight line
You would have to spin the source quite quickly to have an noticable 'curvature' of the light, or be viewing it over a very large scale.
You also need somethign to scatter the light, you can't see a light beam heading away from you. What slightly complicates the picture for the light is that you also have to take into account the time taken for the light to reflect off the medium and reach your eye - so you would only see the correct pattern if you were directly overhead.
There is a similar effect to this seen in reality where jets of light from a spinning star illuminate the surrounding gas