Yes, it will happen, but the radius of the effect is simply too small to see it.
You are only bending a minute faction of the light from the star traveling toward you. It's not enough light to see, and it's too small to resolve (unless you could resolve the black hole in the first place).
Think about it: The redirected light only has the "size" of the gravitation field in question. For an earth sized mass thats 9mm. Even if you did 9km (which wouldn't bend much) you couldn't see it, never mind 9mm.
You are only bending a minute faction of the light from the star traveling toward you. It's not enough light to see, and it's too small to resolve (unless you could resolve the black hole in the first place).
Think about it: The redirected light only has the "size" of the gravitation field in question. For an earth sized mass thats 9mm. Even if you did 9km (which wouldn't bend much) you couldn't see it, never mind 9mm.