Earlier quoted context omitted.
Google accounts actually came out several years before Google+. I remember that Google already had a unified account system across all products before I started working for them; I think they rolled it out in 2008. Google+ didn't launch as a destination site until 2011.
As far as I can remember Google services required a Gmail account before Google+. Here is Schmidt commenting about the release of Google+ as an identity service. http://www.forbes.com/sites/kashmirhill/2011/08/29/googles-e...
http://blogoscoped.com/forum/164385.html
http://www.computerworld.com/article/2517360/security0/repor...
The "G+ is just an identity layer on top of Google" was a common soundbite reported by executives at the time, and perhaps they even believed it, but my engineers-level view as someone who worked with the G+ codebase was that this was mostly marketing speak to differentiate us from Facebook and deflect criticism of "Well, if G+ is a new social network, why would I use it over Facebook?" By saying it's the identity layer for Google, they can then say "Well, you use Google already, this is just the social layer that ties all Google products together." On a technical level a "G+ account" was just a bit set in your Gaia record that indicated whether you had opted in to G+ features.