Google did not respond to requests for comment.

But the day after Google software engineer Steve Yegge a rant about Google's management and handling of Google+ on the social network, Schmidt has an account and has made a few posts.

"To me, Schmidt's move to Google+ is pretty obvious and transparent," said Dan Olds, an analyst with The Gabriel Consulting Group. "Google+ has received some bad publicity surrounding the low number of who use the site. Add in the frank comments of a Google engineer, who wrote a devastating and frank critique to Google's Google+ approach, and starting up a Google+ account suddenly ranks pretty high on Google executives' to-do lists."

Both Olds and Rob Enderle, an analyst with the Enderle Group, said it looks bad for a company's executives not to use its big products.

"Honestly I think that executives who run a company and can, but choose not to, use that company's products, should be replaced by executives who have a passion for what the company builds," Enderle said. "It showcases a disconnect between the executives and the firm's products and helps explain the low ... quality of Google's newer products. "