Is it possible to be connected to Chrome with one account but have another account set has my first account for Gmail (and Google)?
I already know how to use several Google accounts for Chrome and switch between them, and how to use several Google accounts for Gmail and switch between them, but I couldn't find anything on the Web for my specific question.
You can achieve a close result using the simple trick of cusomizing Chrome's "New tab" setting.
And to achieve this, I personnaly use the extension "New Tab Redirect" (but you could also use "Custom New Tab URL", or "New Tab Changer").
For your new tabs, assuming that you'd want to use the second account you connected with on Google, specify this for the URL: https://www.google.com/?authuser=1 for Google's main page (or https://mail.google.com/mail/u/1 for GMail ).
(If you'd want to use your third account, you would use, /?authuser=2 or /u/2, and so on.)
Hope that helps.