I don't think so.... If they are in a lot of pain I can see how that might make them throw up. Have you tried Tylenol to take the pain away? And how bad is it? If it keeps up you should call the doctor.
Oh no I have never heard of that...if you think its pain related get your baby some teething tablets you rub them on the gums like a paste and it numbs the mouth for a while...but other than that i can see no reason for the vomiting..you should call your doctor