It depends. Sometimes they grow out of it, sometimes not. I discovered Jackson's overbite at his first vet visit at 12 weeks old. At 3 years old, he had been having issues for a while that I had noticed but it had gotten worse... he kept opening and closing his mouth like he was uncomfortable. It always hurt him worse in the mornings. So I decided I finally had to have something done. His bottom canine tooth was poking into his upper palate/roof of his mouth.
The vet told us that she technically could pull his canine tooth but she did not recommend it, since the root is so long etc. She referred us to a veterinary dentist, and we ended up deciding on doing a vital pulpotomy. They basically shaved the tooth down and then had to 'fill it'. It was great to see him not in pain anymore or uncomfortable, despite the hefty $1300 price tag! It was good I did it when I did too because it was making a hole in the roof of his mouth and was soon going to be up his nasal cavity. Because he was so young, they said the skin would grow back and he would be fine.
Of course many pups have overbites and don't have this issue! It just figures that Jackson's slight over-bite was juuustt enough to cause an issue. It was only on one side of his mouth too, because when he was a pup, he had the 'double row' of teeth... his baby teeth were still in when the adult canines were coming in. So it kind of made that one tooth crooked and I think that's where the issue came in.
You can see the shaved down canine tooth here