Nope, look it up. Google has never taken out an advertisement in radio, magazine, television, newspaper, or even through banner ads on the Internet in order to promote their search. The ONLY ad's Google has ever bought were local legal announcements as required by law (for things like their business license, IPO, and such), to attract applicants for certain open jobs they needed to fill, and to make a public announcement here and there. They have NEVER marketed the search engine itself.
And they grew to dominate the industry while their competitors, including Yahoo, MSN, Lycos, and Altavista, were spending tens of millions of combined dollars to attract viewers to their sites via television, radio, and print. Google beat them ALL through basic word of mouth promotion because their product was simply BETTER.