Truth is that nearly all restaurant critics who are worth anything are easily recognized in their own cities or, in a place as small as Israel, in most restaurants. Another truth is that does not really help the chef....
Certainly the recognized critic can get better service but knowing that the critic watches carefully to observe the service at tables other than his/her own. Can also get a large portion, but here again, one watches to see what portions others are receiving.
Also, as chefs have their tricks, so do critics. Order the soup, for example...that was made long before the critic appeared and there is nothing the chef can do about that; the same with many sauces; and certainly with desserts. Order the most standard things on the menu as those give an easy basis for comparison. Also order at least one or two of the chef's specialties to judge how creative he/she can be.
And don't forget, when a well known critic is known to be on the premises the chef and the waitstaff are nervous and thus bound to make quite a few small but serious errors.