I don't really think so. When was the last time "Ads by Google" became something people used to discover that nifty search engine? I really can't imagine that. "Hay look it lez me find things!"
I know I wouldn't be aware of their omnipresence as much if they didn't write "Ads by Google" alongside their ads. Insofar as ads is about building brand recognition and I recognize Google better, then "Ads by Google" is an ad within the ad from my perspective (by the way I'm 100% for it).
They've gotten some publicity - remember the ad that was like {first 10 digit prime found in consecutive digits of e}.com?
But for the most part they haven't really advertised in the traditional way. Instead, they've used the best form of advertising - make a product so good that it speaks for itself!
"Ads by Google" alongside most ads on the internet doesn't count as google advertising its brand?