No, Billy Black is consistently portrayed as being confined in his wheel chair.  Whenever he does need to go somewhere, Jacob has to drive him.  You may be getting him confused with one of the other characters on the reservation, like Harry Clearwater, Seth and Leah's dad.  One of the elders of the Quileute tribe like Billy, Harry Clearwater is also a good friend to Bella's father, Charlie Swan; both men enjoy fishing together.  Harry has a heart attack in New Moon, and the news of his death serves as the catalyst for Edward's decision to go to the Volturi.