Well, contrary to what many people believe, the answer is – no it cannot. Installing Google toolbar does not cause the pages to be indexed. Matt Cutts writes on his blog that it is almost impossible to keep a web server secret by not publishing any links to it.
According to Google: "As soon as someone follows a link from your "secret" server to another web server, your "secret" URL may appear in the referrer tag and can be stored and published by the other web server in its referrer log. So, if there's a link to your "secret" web server or page on the web anywhere, it's likely that Googlebot and other web crawlers will find it."
Matt's blog post talks about the experiment carried to ascertain whether toolbar affects page ranking or not. The experiment obviously fails to prove so.