Two of my three were thumb suckers, and I will say they didn't naturally grow out of it -- but they needed to be mentally prepared to stop and that didn't happen at two years old. For your son, the thumb is his comfort item -- like a "blankie" or favorite stuffed animal. He is not going to stop at age 2 and you shouldn't expect him to.
My eldest daughter stopped (the first time) when she was 4, but start again about 5 months later when her little sister was born. It took a couple of more years to get her to completely stop. At that age, she only did it in her sleep which was the hardest thing to stop.
My second daughter also sucked her thumb. She was about 5 when she completely gave up the habit.
Did I like it? No! Did I need to cause myself and my children unnecessary stress over it! Double NO!
Did both my girls wind up needing braces? Yes! The oldest one was most likely because of her thumb sucking, but not my other daughter -- they sucked their thumbs differently (so I'm told) and it didn't create problems for her.
Your son is not necessarily ruining his teeth, and highly unlikely his palate. Neither of my daughters had any palate issues (funny thing is their cousin did, yet she didn't suck her thumb!).
I use to stress out about it with my oldest, but in the end learned to relax.
Your son may not "grow out of it" but he needs to be mentally ready to give it up so that your efforts are successful with minimal stress.