Student or Learner
Koreans have a Korean-style English expression like "He did overeat yesterday", which means "He threw up(vomitted) after heavy drinking", and I've always considered this as broken English, but I happened to find "overeat oneself sick".
Anyway, "overeat" is never related to "vomitting", right?
You can overeat (eat too much but not necessarily be sick as a result) or you can eat yourself sick (sickness being a result of eating). *Overeat yourself sick is not used because syntactically, the prefix over- does not go with the resultative phrase yourself sick.