No, but you will get "Thousand islands" sauce.

Oddly enough, in my part of the country, a mixture of ketchup and mayonnaise is called "Russian dressing." I don't want to disagree with shevelen8, and "Thousand Islands" dressing is similar, but "Russian dressing" as my mom made it, growing up near New York City, is smooth, while "Thousand Islands dressing" is full of chopped-up onions, pickles, chives, and other things.