As soon as I read the title of your post I thought to myself: "I'll bet her son is about 5 or 6." LOL
Yep, my son did that too. I even vaguely recall doing that myself! My daughter really never was a chewer of her shirt, but she chews her fingers (cuticles---I have had issues with this myself as well). I think the shirt chewing is fairly normal and common and probably a stress reliever for him. My son ruined a few good shirts (he was in private school and had to wear collared shirts--so no Tshirts were ruined during the making of his elementary experience). But he also outgrew it over time. I think it only lasted for one grade... Maybe first or 2nd grade? Can't really remember which one, now. That seems so long ago... :(
The bandana would probably work really well. Make sure you give him several, because you will want to wash them after each day of school. The only thing I would caution about the bandana is to tell your son up front not to "share" it with his friends. Something "cool" like that might get passed around in a show of friendship, and I don't think you'd want him chewing on stuff other kids have been wearing.
Good luck. He'll be past this in no time.