Not even close. I can't even count the number of people who are familiar with android but have never heard of Linux. Even a fair number of people who know of Linux were surprised when I told them android was based on the Linux kernel. Google doesn't exactly go out of its way to say that android is based on Linux. I've also read a number of articles about smartphones and android in major publications like Newsweek or Business Week, and they rarely, if ever, mention any relation between Android and Linux, or even mention Linux in the article at all.
Android is one thing, but desktop Linux is another. Many people have heard of android or perhaps Linux on embedded devices or servers, but not Linux on desktops PCs. "I thought Linux was for servers."