If it could get it in it's mouth, it is a possibility. Though it is usually carpet anemones that are bad about eating fish, any technically can. Usually it only happens to a sick fish besides carpet nems. I would keep looking as depending on what type of goby it is, it may jsut be hiding. i once went 2 months without seeing a YWG in a 10 gallon tank.
Depends the goby I suppose. The only fish I knew of that really needed a twice a day feeding was anthias. I feed my about every third day and he is fine. There may be a type of goby that has a high enough metabolism that needs more frequent feeding though.