Unlike earth, the curvature is upward, rather than downward, so you certainly wouldn't have an horizon. But how far could you see?
Well when you look into the sky at night, you are looking through an atmosphere, which is fairly transparent. Even with haze, you get plenty of light.
In a Dyson sphere, you'd be looking through two atmopsheres, which isn't so different. So in theory, yes you would be able to see other parts of the sphere.
Second question is illumination. Are the distant parts of the sphere bright enough to see?
Well, all parts of the sphere receive a uniform level of illumination from the star.
So all surface elements reflect the same amount of light.
Now suppose these reflections are diffuse. This means that reflected light is evenly in any reflected direction.
Compare two surface elements - one twice as far away as the other. The surface element twice as far away appears 1/4 area, and its light is spread inverse square, so reflects 1/4 as much light to you, the observer.
However, this lesser area is compensated for by the fact that the Dyson sphere is continuous, so distant parts of the sphere appear as bright a those nearby.
Looking at low angles does mean that light is travelling through more atmosphere, so there is more hazing.
Overall, looking up, you see the star directly overhead, and around it you see the far side of the sphere, reflecting as bright as the ground you stand on looking down.
Looking at lower angles, you see layer of haze, where the view may be fuzzy or grayer or duller compared to what is nearby. Looking over that haze, you see a wall in the distance, like mountains pushing up through the clouds - except that this is far side of the sphere extending up towards the star, again appearing just as bright as the land beneath your feet.
I hope that helps you visualise it.