No, they can get bigger than the mare. My mom bought a QH weanling who's dam was 14.2hh and sire was 15.1hh and when he finished growing he toped out at 16hh.
I think 13hh isn't stunted for a 9 month old. I once got an Arab yearling who's growth was stunted and he was the size of an average weanling for his breed. His was definitely the case of lack of proper nutrition. He was being fed in a tiny stall with two QH yearlings and couldn't compete. He also was never wormed and had a horrible wormy pot belly.
Good luck with your guy, he should get to be a nice size for you.
[COLOR=DarkRed]Well behaved women rarely make history!
Fpzipsdreammachine "Booty" 2006 AQHA mare