Absolutely it will, we have had several over the years that had similar happen and they're 30 ft. tall now. Key is to get rid of the dead stuff so the new has room to grow in that direction. Ours you cannot even tell that is what happened to them now that they're older.
So how are everyone's Apple trees doing this year? Mine are hammerin' and heavy with fruit. I do have a couple that are struggling so they will get a shot of miracle grow here soon. My pear trees are crazy loaded
I have 3 year old apple, persimmon, and pear, about 6'' tall but I have been aggressively cutting off the tops to keep them short. I had flowers this year for the first time but I don't think anything produced yet. My grape vines have a million baby grapes. Its fun to plant from sprouts and watch them grow. I'm trying to grow some apples in my window from apple seeds and a McDonald's milk shake cup.