Question

If gravity did not affect the pain of a horizontally thrown ball the ball would

Answer 1

If gravity did not affect a horizontally thrown ball, the ball would continue along its horizontal path indefinitely (assuming it is thrown in a vacuum so no other forces are acting on it).

Answer 2

If gravity had no effect on a ball after you threw it ... and there also
were no air to slow it down ... then the ball would continue traveling
in a straight line, in whatever direction you threw it. 

That's the heart and soul of Newton's laws of motion ... any object
keeps moving at the same speed, and in a straight line in the same
direction, until a force acts on it to change its speed or direction.\

If you threw the ball horizontally, then it would keep moving in the
same direction you threw it.  But don't forget:  The Earth is not flat.
The Earth is a sphere.  So, as the ball kept going farther and farther
in the same straight line, the Earth would curve away from it, and it
would look like the ball is getting farther and farther from the ground.