Will training with a small ball or a size 1 soccer ball still get you to improve? Yes, definitely. I love incorporating a smaller soccer ball in my first touch sessions or tight space dribbling sessions to improve my touch and control of the ball. Now, you shouldn't ALWAYS train with a small ball, because I'm a firm believer in that you should practice how you play, but still there are huge benefits to training with a smaller sized soccer ball especially in terms of developing control/touch.
Use a Tennis ball with these drills to get your brain and body in sync so that when you go back to using a normal Soccer ball, you will feel comfortable and be able to perform ball mastery skills even better than before.